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Physical chemistry 物理化学Thermodynamics [,θɜːmə(u)dai'næmiks] n 热力学Kinetics [ki'netiks; kai-] n 动力学Quantum chemistry 量子化学Statistical mechanics 统计力学Mechanism ['mek(ə)niz(ə)m] n 机理Equilibrium of Heterogeneous SubstancesColloid and surface chemistry 胶体表面化学Quantum mechanics 量子力学Infrared spectroscopy 红外光谱Microwave spectroscopy 微波光谱EPR spectroscopy电子顺磁共振波谱法NMR spectroscopy 核磁共振谱Nuclear chemistry核化学Astrochemistry 天体化学Surface chemistry 表面化学Mechanical work 机械功Zero law of thermodynamics 热力学第零定律law of thermodynamics 热力学定律entropy ['entrəpi] n 熵system ['sistəm] n 系统surrounding [sə'raundiŋ] n 环境internal energy 内能thermodynamic potential 热力位（势）equilibrium [,iːkwi'libriəm; ,ekwi-] n 平衡spontaneous process 自发过程Zeroth law 第零定律Energy balance equation 能量守恒方程Legendre transformation勒让德变换Enthalpy ['enθ(ə)lpi; en'θælp i] n 焓Helmholtz energy 亥姆霍兹自由能Gibbs energy 吉布斯自由能Isolated system 孤立系统Adiabatic system 绝热系统Diathemic system 透热系统Closed system 封闭系统Open system 开放系统Thermodynamic equilibrium 热力学平衡Reversible process 可逆过程Definite state定态Intensive variable 强度变量Extensive variable 广度变量Equation of state 状态方程Thermodynamic process 热力学过程Isobaric [,aisə'bærik] adi 等压的Isochoric[,aisəu'kɔ:rik]/ isometric[aisə(u)'metrik]/ isovolumetric [,aisəu,vɔlju'metrik] adj 等容的Isothermal [,aisəu'θɜːməl] adj 等热的Adiabatic [,eidaiə'bætik; ,ædiə-] adj 绝热的Isentropic [,aisen'trɔpik] adj 等熵的Isenthalpic [,aisən'θælpik] adj等焓的Steady state 稳态Phase rule 相律Phase diagram 相图Phase [feiz] n 相Density ['densiti] n 密度Index of refraction 折射率Chemical composition 化学组成Plasma ['plæzmə] n 等离子体Polar ['pəulə] adj 极性的Non-polar 非极性的Phase transition 相转变Triple point 三线点Solidus 固相线Liquidus 液相线Critical point 临界点Supercritical fluid 超临界流体Non-azeotropic 非共沸的Binary phase diagram 二元相图Eutectic [juː'tektik] adj 低共熔的,共熔的n 共熔合金Peritectic [,perə'tektik] adj 包晶体的（转熔的）n 包晶Boiling point diagram 沸点图Chemical kenetics 化学动力学Reaction rate 反应速率Effect of various variables 各种变量的影响P181Re-arrangement of atom 原子重排Formation of intermediate 中间体的形成Law of mass action 质量作用定律Zero-order 零级First-oder 一级Second-order 二级Rate-determining step决速步Activation energy 活化能Arrhenius equation 阿伦尼乌斯方程Eyring equation 艾琳方程Physical state 物理状态Concentration [kɔns(ə)n'treiʃ(ə)n] n 浓度Catalyst ['kæt(ə)list] n 催化剂Autocatalysis [,ɔːtəukə'tælisis] n 自催化作用Enzyme ['enzaim] n 酶Michaelis-Menten kinetics 米夏埃利斯-门滕动力学Partial pressure 分压Electrochemistry [i,lektrəu'kemistri] n 电化学Electrolysis [,ilek'trɔlisis; ,el-] n 电解Electrochemical reaction 电化学反应Oxidation/reduction reaction 氧化/ 还原反应Electrochemical cell 电化学电池Galvanic cell 伽伐尼电池，原电池V oltaic cell 伏达电池Anode ['ænəud] n 阳极Cathode ['kæθəud] n 阴极Electrical battery 电池Primary battery 原电池，一次电池Secondary battery 蓄电池，充电电池Electroform [i'lektrəufɔːm] v 电铸Electroplate [i'lektrə(u)pleit; i,lektrə(u)'pleit] v 电镀Electrowinning [i,lektrəu'winiŋ] n 电解冶金法，电积金属法Electrorefine 电解精炼，电精制Corrosion [kə'rəuʒ(ə)n] n 腐蚀，锈蚀Passivation [pæsi'veiʃən] n 钝化Plate [pleit] v 电镀Cathodic protection 阴极保护Surface science 表面科学Surface chemistry 表面化学Surface physics 表面物理Surface engineering 表面工程Interface 界面Colloid science 胶体科学Adsorption [æd'sɔ:pʃən] n 吸附Chemisorption [kɛmi'zɔrpʃən] n 化学吸附Physisorption [,fizi'sɔ:pʃən] n 物理吸附Colloid chemistry 胶体化学Dispersed phase 分散相Continuous phase 连续相Aerosol ['eərəsɔl] n 气溶胶Emulsion [i'mʌlʃ(ə)n] n 乳液Foam [fəum] n 泡沫Dispersion [di'spɜːʃ(ə)n] n 分散体系Hydrosol ['haidrəusɔl] n 水溶胶Tyndall effect 丁达尔效应Stability of colloid system 胶体系统的稳定性Steric stabilization 位阻稳定Electrostatic stabilization 静电稳定作用Buoyancy ['bɔiənsi] n 浮力Floc [flɔk] n 絮状物Flocculant ['flɑkjələnt] n 絮凝剂Depletant n 耗尽剂Suspension [sə'spenʃ(ə)n] n 悬浮液Brownian force 布朗力Viscoelastic [,viskəui'læstik] n 粘弹性的Lattice ['lætis] n 点阵Pattern 图样，模，型式，图，特性，图案Unit cell 晶胞Lattice parameter 晶格参数Miller index notation 密勒指数Orthogonal [ɔː'θɔg(ə)n(ə)l] adj 正交的Optical property 光学性质Adsorption and reactivity 吸附和反应性Surface tension 表面张力Microstructural defect 微结构缺陷Cleavage ['kliːvidʒ] n 裂缝，分裂Plastic deformation 塑性变形Burgers vector 伯格斯矢量Inherent symmetry 固有对称性Two fold rotational symmetry 二重旋转对称Mirror plane symmetry镜面对称Translational symmetry 平移对称Compound symmetry 复合对称Cubic ['kjuːbik] adj 立方的Hexagonal [hek'sæɡənəl] adj 六方的Tetragonal [ti'træg(ə)n(ə)l] adj 四方的Rhombohedral [rɔmbəu'hi:drəl] adj 菱形的Orthorhombic [,ɔːθə(u)'rɔmbik] adj 正交晶的，斜方的Monoclinic [mɔnə(u)'klinik] adj 单斜的Triclinic [trai'klinik] adj 三斜的Bravais lattice 布拉维点阵Space lattice 空间点阵Quasicrystal ['kweizai'kristl] n 准晶体Point group / crystal class点群Reflection [ri'flekʃ(ə)n] n 反射Rotation [rə(u)'teiʃ(ə)n] n 旋转Inversion [in'vɜːʃ(ə)n] n 反衍Improper rotation 非正常旋转，反射旋转Rotation axe 旋转轴Reflection plane 反射面Center of symmetry 对称中心Symmetry element 对称元Space group 点群Pure translation 纯平移，纯平动Screw axe 螺旋轴Glide plane 滑动面。
高三英语学术成果单选题50题1. In the scientific research paper, the new discovery was described as "a ______ breakthrough that could change the future of medicine."A. crucialB. criticalC. acuteD. severe答案：A。
本题考查词汇辨析。
crucial表示至关重要的，在描述突破对医学未来的影响时，表达其关键重要性；critical也有批判的、关键的意思，但更多用于批判性的情况或危机时刻，在这里不如crucial合适；acute主要指尖锐的、敏锐的或者急性的（疾病等），与语境不符；severe表示严重的，多形容程度恶劣，不适用于描述突破的重要性。
2. The history article mentioned that during the war, the city faced a ______ shortage of food.A. severeB. strictC. rigidD. stern答案：A。
解析：severe表示严重的，用来形容食物短缺的程度非常严重，符合语境；strict侧重于严格的，常指规定、纪律等严格；rigid表示僵硬的、死板的，多形容物体或者规则缺乏灵活性；stern主要指严厉的，多形容人的态度，这三个选项均不符合食物短缺的语境。
3. In the literary analysis, the author's use of symbolism was very ______, adding deep meaning to the story.A. subtleB. delicateC. faintD. weak答案：A。
答案解析：subtle表示微妙的、隐晦的，在文学分析中，作者对象征手法的使用很微妙，给故事增添深意，是合适的表达；delicate指精致的、娇弱的，更多形容物体的外观或者人的身体状况等；faint表示微弱的、模糊的，多形容声音、光线等；weak表示虚弱的、薄弱的，不适合形容象征手法的运用。
熵概念辨析EntropyCao Zexian中国科学院物理研究所内容提要¾热力学基础知识回顾¾Emergent Phenomenon¾Entropy和熵的字面意思¾熵概念－伤脑筋¾Entropy的数学表达¾Entropy 概念上的伟大成果量子力学的诞生；光子的极化态自旋薛定谔方程的推导；信息论¾Entropy作为过程的判据？¾结束语热力学是怎样的一门学问？我在德国Kaiserslautern大学机械系一间实验室的窗框上读到过这样的一段话，大意是：“热力学是这样的一门课：你学第一遍的时候觉得它挺难，糊里糊涂理不清个头绪，于是，你决定学第二遍；第二遍你觉得好像明白了点什么，这激励你去学第三遍；第三遍你发现好像又糊涂了，于是你只好学第四遍。
等到第四遍，well, 你已经习惯了你弄不懂热力学这个事实了。
”但我们必须理解热力学，因为：¾热力学是真实的。
Nothing in life is certain except death, taxes and the second law of thermodynamics. －Seth Lloyd¾热力学就在身边。
In this house, we obey the laws of thermodynamics! -Dan Castellaneta¾热力学是必备知识。
知冷知热是确立配偶人选的基本判据。
－曹则贤P. W. Anderson: More is different曹则贤，熵非商：the myth of Entropy,《物理》第九期，Entropy的字面意思Tropy的字面意思tropik<tropicus< Gr tropikos,belonging to a turn(of the sun at the solstices)Tropic of Cancer（北回归线）Tropic of Capricorn （南回归线）)Heliotropism: 向日性。
材料科学，主要包含金属、陶瓷、复合材料等，高分子的一般是在化学里面。
1。
acta materialia这个应该算是材料科学中影响力最大的期刊了吧，。
2002 年的if是3.104。
1953年开始的。
原来封面是4个圈的，2004年中间开始多了一个圈（theory）。
paper都很长的，大都在7page以上吧，现在没有letters的。
同一个出版社的还有个scripta materialia。
Acta Materialia's purpose is to publish original papers and occasional critical reviews which advance the understanding of the structural and functional properties of materials: metals and alloys, ceramics, high polymers and glasses. Emphasis is placed on those aspects of the science of materials that are concerned with the relationship between the structure of solids and their properties (mechanical, chemical, electrical, magnetic and optical); with the thermodynamics, kinetics and mechanisms of processes occurring within solids; with experiments and models which help in understanding the macroscopic properties of materials in terms of microscopic mechanisms; and with original work which advances the understanding of structural and functional materials./JournalDetail.html?PubID=221&Precis=DESC/science/journal/135964542。
German mathematicians have made significant contributions to the field of mathematics throughout history.Here are some notable figures and their achievements:1.Carl Friedrich Gauss17771855:Often referred to as the Prince of Mathematicians, Gauss made groundbreaking contributions to number theory,algebra,statistics,analysis, differential geometry,geodesy,geophysics,mechanics,electrostatics,magnetic fields, astronomy,matrix theory,and optics.His work on the Fundamental Theorem of Algebra and the Gaussian distribution are particularly influential.2.Georg Cantor18451918:Cantor is best known for his work on set theory,which has become a fundamental theory in mathematics.He introduced the concept of infinite sets and cardinality,challenging the traditional notion of infinity with his discovery of different sizes of infinity.3.David Hilbert18621943:Hilbert was a prominent mathematician who made significant contributions to algebra,number theory,and geometry.He is famous for his list of23 unsolved problems,presented in1900,which guided much of the mathematical research for the following century.4.Leopold Kronecker18231891:Kroneckers work in algebra,particularly his contributions to number theory and algebraic structure,laid the groundwork for modern algebra.He is known for his belief that God made the integers all else is the work of man.5.Bernhard Riemann18261866:Riemann is renowned for his work in complex analysis and number theory.His most famous contribution is the Riemann Hypothesis,one of the most important unsolved problems in mathematics,which concerns the distribution of prime numbers.6.Felix Klein18491925:Klein made significant contributions to geometry,particularly in the field of nonEuclidean geometry.His Erlangen Program classified geometries by their underlying group of symmetries,which has had a profound impact on the development of modern geometry.7.Sophie Germain17761831:Although not as wellknown as her male counterparts, Germain was a pioneering female mathematician who made important contributions to number theory and elasticity.She is known for her work on Fermats Last Theorem and for her correspondence with Gauss.8.Hermann Minkowski18641909:Minkowski was a key figure in the development of the mathematical theory of relativity.His concept of spacetime,which combines the threedimensions of space with the fourth dimension of time,was crucial for Einsteins theory of special relativity.9.Ernst Eduard Kummer18101893:Kummer made significant contributions to number theory,particularly in the area of prime numbers.His work on the theory of ideals in rings laid the foundation for modern algebraic number theory.10.Max Planck18581947:Although best known for his work in physics and the development of quantum theory,Planck also made contributions to mathematics, particularly in the areas of thermodynamics and statistical mechanics.These mathematicians,among others,have shaped the course of mathematics and continue to influence the field with their theories and discoveries.Their work has not only expanded our understanding of the mathematical universe but has also had practical applications in various scientific and technological advancements.。
International Journal of Project Management , Volume 28, Issue 3,April 2010, Pages 285-295Paul Bowen, Peter Edwards, Keith Cattell, Ian JayShow preview | Related articles | Related reference work articlesPurchase85Dynamics of R&D networked relationships and mergers and acquisitions in the smart card field Original ResearchArticleResearch Policy , Volume 38, Issue 9, November 2009,Pages 1453-1467 Zouhaïer M’ChirguiClose preview | Related articles | Related reference work articlesAbstract | Figures/Tables | ReferencesAbstractThis paper analyzes how the structure and the evolution of inter-firmagreements have shaped the development of the smart card industry. The aimis to establish a closer connection between the evolution of inter-firmagreements in the smart card industry and the patterns of change of technologyand demand in this new high-tech industry. Based on a proprietary databasecovering both collaborative agreements and mergers and acquisitions (M&As)occurring in this industry over the period 1992–2006, we find that the evolutionof technology and market demand shapes the dynamics of R&D networks andPurchaseM&As are likely to change the industry structure. We also find that a small group of producers – first-movers – still control the industry and technological trajectories. Their position arises not for oligopolistic reasons of marketstructure, but for technological and organizational reasons.Article Outline1. Introduction2. Theoretical background3. The smart card industry: delineating the boundaries and identifying the actors3.1. Defining the smart card3.2. The differentiated market(s)3.3. The actors3.4. The smart card oligopoly: a dual market structure4. Research methods4.1. Methodology4.2. SCIFA database5. Trends in inter-firm agreements and emergence of networks in the smart cardindustry6. The structure of the network6.1. Network evolution6.2. Major players and centrality7. ConclusionAcknowledgementsReferences86The role of industrial maintenance in the maquiladoraindustry: An empirical analysis Original Research ArticleInternational Journal of Production Economics, Volume 114,Issue 1, July 2008, Pages 298-307Shad DowlatshahiClose preview | Related articles | Related reference work articlesPurchaseAbstract | Figures/Tables | ReferencesAbstractThis study explored the role of industrial maintenance in the maquiladora industry. The maquiladora industry is a manufacturing system that utilizes the Mexican workforce and foreign investment and technology on the border region between the United States and Mexico. The issues related to industrial maintenance were studied through a survey instrument and 11 in-depth and extensive field interviews with experts of eight maquiladora industries in El Paso, TX and Juarez, Mexico. Based on an 86% response rate (with 131 usable questionnaires) and four major survey questions, statistical analyses were performed. The survey questions included: collaboration between the maintenance and other functional areas, likely sources of maintenance problems (equipment, personnel, and management), major common losses of maintenance problems, and the role of ISO certification in maintenance. Finally, additional insights and assessment of the results were provided.Article Outline1. Introduction1.1. Review of literature2. Evolution of and various approaches to maintenance3. Historical, operational characteristics and the importance of the maquiladora industry4. Research design4.1. Data collection4.2. The interviews with maquiladora managers5. Analyses of results5.1. Statistical analysis for question 15.2. Statistical analysis for question 25.3. Statistical analysis for question 3 5.4. Statistical Analysis for question 46.Conclusions and assessmentReferences87 A variable P value rolling Grey forecasting model forTaiwan semiconductor industry production OriginalResearch ArticleTechnological Forecasting and Social Change, Volume 72,Issue 5, June 2005, Pages 623-640Shih-Chi Chang, Hsien-Che Lai, Hsiao-Cheng YuClose preview | Related articles |Related reference work articlesAbstract | Figures/Tables | ReferencesAbstractThe semiconductor industry plays an important role in Taiwan's economy. In thispaper, we constructed a rolling Grey forecasting model (RGM) to predictTaiwan's annual semiconductor production. The univariate Grey forecastingmodel (GM) makes forecast of a time series of data without considering possible correlation with any leading indicators. Interestingly, within the RGM there is aconstant, P value, which was customarily set to 0.5. We hypothesized thatmaking the P value a variable of time could generate more accurate forecasts. Itwas expected that the annual semiconductor production in Taiwan should beclosely tied with U.S. demand. Hence, we let the P value be determined by theyearly percent change in real gross domestic product (GDP) by U.S.manufacturing industry. This variable P value RGM generated better forecaststhan the fixed P value RGM. Nevertheless, the yearly percent change in realGDP by U.S. manufacturing industry is reported after a year ends. It cannotserve as a leading indicator for the same year's U.S. demand. We found out thatthe correlation between the yearly survey of anticipated industrial productiongrowth rates in Taiwan and the yearly percent changes in real GDP by U.S. manufacturing industry has a correlation coefficient of 0.96. Therefore, we usedPurchasethe former to determine the P value in the RGM, which generated very accurate forecasts. Article Outline1.Introduction2. The semiconductor industry in Taiwan3. Rolling GM (1,1)4. Forecast Taiwan semiconductor production with RGM (1,1)5. Forecast Taiwan semiconductor production with variable P value RGM (1,1)6. ConclusionsAppendix A. AppendixA.1. 1998 Production forecast for the semiconductor industry under different PvaluesA.2. 1999 Production forecast for the semiconductor industry under different PvaluesA.3. 2000 Production forecast for the semiconductor industry under different PvaluesA.4. 2001 Production forecast for the semiconductor industry under different PvaluesA.5. 2002 Production forecast for the semiconductor industry under different PvaluesReferencesVitae88 Energy demand estimation of South Korea using artificial neural network Original Research ArticleEnergy Policy , Volume 37, Issue 10, October 2009, Pages4049-4054Zong Woo Geem, William E. Roper Close preview | Related articles | Related reference work articlesAbstract | Figures/Tables | ReferencesPurchaseAbstractBecause South Korea's industries depend heavily on imported energy sources (fifth largest importer of oil and second largest importer of liquefied natural gas in the world), the accurate estimating of its energy demand is critical in energy policy-making. This research proposes an artificial neural network model (a structure with feed-forward multilayer perceptron, error back-propagation algorithm, momentum process, and scaled data) to efficiently estimate the energy demand for South Korea. The model has four independent variables, such as gross domestic product (GDP), population, import, and export amounts. The data are obtained from diverse local and international sources. The proposed model better estimated energy demand than a linear regression model (a structure with multiple linear variables and least square method) or an exponential model (a structure with mixed integer variables, branch and bound method, and Broyden–Fletcher–Goldfarb–Shanno (BFGS) method) in terms of root mean squared error (RMSE). The model also forecasted better than the other two models in terms of RMSE without any over-fitting problem. Further testing with four scenarios based upon reliable source data showed unanticipated results. Instead of growing permanently, the energy demands peaked at certain points, and then decreased gradually. This trend is quite different from the results by regression or exponential model.Article Outline1. Introduction2. Artificial neural network model3. Case study of South Korea4. Results of linear regression model5. Results of exponential model6. Results of ANN model7. Validation of the ANN model8.Future estimation with different scenarios9. ConclusionsReferences89 Catching up through developing innovation capability: evidence from China's telecom-equipmentindustry Original Research ArticleTechnovation , Volume 26, Issue 3, March 2006,Pages359-368 Peilei FanShow preview | Related articles | Related reference work articlesPurchase90 Optimization of material and production to develop fluoroelastomer inflatable seals for sodium cooled fastbreeder reactor Original Research ArticleNuclear Engineering and Design , In Press, Corrected Proof, Available online 16 February 2011N.K. Sinha, Baldev RajShow preview | Related articles | Related reference work articlesPurchase Research highlights► Production of thin fluoroelastomer profiles by cold feed extrusion and continuous cure involving microwave and hot air heating. ► Use of peroxide curing in air during production . ► Use offluoroelastomers based on advanced polymer architecture (APA) for the production of profiles. ► Use of the profiles in inflatable seals for critical application of Prototype Fast Breeder Reactor. ► Tailoring of material formulation by synchronized optimization of material and production technologies to ensure that the produced seal ensures significant gains in terms of performance and safety in reactor under synergistic influences of temperature, radiation, air and sodium aerosol.91 The dynamic transfer batch-size decision for thin film transistor –liquid crystal display array manufacturing by artificialneural-network Original Research ArticleComputers & Industrial。
2024年高三英语统计学分析单选题30题1.The average height of a group of people is calculated by adding up all the heights and then dividing by the _____.A.number of peopleB.sum of heightsC.difference in heightsD.product of heights答案：A。
本题考查平均数的计算方法。
平均数是所有数据之和除以数据的个数，这里就是把所有人的身高加起来然后除以人数。
选项B“sum of heights”是身高总和，不是计算平均数的除数。
选项C“difference in heights”是身高差，与平均数计算无关。
选项D“product of heights”是身高乘积，也与平均数计算无关。
2.In a statistical survey, the mode is the value that _____.A.appears most frequentlyB.has the highest sumC.is the averageD.is the middle value答案：A。
本题考查众数的概念。
众数是一组数据中出现次数最多的数值。
选项B“has the highest sum”是和最大，与众数无关。
选项C“is the average”是平均数，与众数不同。
选项D“is the middle value”是中位数，不是众数。
3.The median of a set of data is found by arranging the data in orderand then finding the _____.rgest valueB.smallest valueC.middle valueD.average value答案：C。
⼟⽊⼯程专业英语1Civil engineering(⼟⽊⼯程)Civil Engineering. Civil engineering,the oldest of the engineering specialties,is referring to the planning, design, construction, and management of the built environment. This environment includes all structures built according to scientific principles,from irrigation and drainage systems to rocket-Jaunching facilities.Civil engineers build roads, bridges, tunnels, dams, harbors, power plants, water and sewage systems, hospitals, schools , mass transit, and other public facilities essential to modern society and large population concentrations..They also build privately owned facilities such as airports, rail-roads , pipelines, skyscrapers , and other large structures designed for industrial, commercial, or residential use. In addition, civil engineers plan, design, and build complete cities and towns, and more recently have been planning and designing space platforms to house self-contained communities.The word "civil" derives from the Latin for citizen. In 1782, an Englishman named John Smeaton used the term to differentiate his nonmilitary engineering work from that of the military engineers who predominated at the time. Since then, the term "civil engineering" has often been used to refer to engineers who build public facilities, although the field is much broader. Scope.It is so broad, that civil engineering is subdivided into a number of technical specialties.Depending on the type of project, civil engineer specialists with many kinds of skills may be needed. When a project begins, the site is surveyed and mapped by civil engineers who locate utility placement-water, sewer, and power lines. Geotechnical specialists perform soil experiments to determine if the earth can bear the weight of the project. Environmental specialists study the project's impact on the local area: the potential for air and groundwater pollution,the project's impact on local animals and plant life,and how the project can be designed to meet government requirements aimed at protecting the environment. Transportation specialists determine what kinds of facilities are needed to ease the burden on local roads and other transportation networks that will result from the completed proj ect. Meanwhile, structural specialists use preliminary data to make detailed designs, plans, and specifications for the project. Supervising and coordinating the work of these civil engineering specialists , from the beginning to the end of the project, are the tasks of the construction management specialists. Based on the information supplied by other specialists, construction management civil engineers estimate quantities and costs of materials and labor, schedule all work, order materials and equipments for the job, hire con.tractors and subcontractors, and perform other supervisory work to ensure the project is completed on time as specified.Throughout any given project, civil engineers make extensive use of computers. Computers are used to design projects' various elements (computer-aided design,or CAD) and manage/doc/1d8a7d266137ee06eef91860.html puters are a necessity for modern civil engineers because they permit engineers to efficiently handle large quantities of data needed in determining the best way to construct a project. NEW WORDS AND PHRASES1.predominate居⽀配地位，统治，（数量上）占优势2.geotechnical岩⼟⼯程的3.specification载明，详述，技术要求，说明书，清单4.supervise监督，管理，控制5．subcontractors转包合同，转包⼯作(6. hurricane飓风，（感情等的）爆发7．asphalt沥青，铺沥青于8．aluminum【化】铝9．runoff⾬量，流量，决赛，决定性竞选10. lock⽔闸，闸门11. fill充⾜，饱满，装填物，（⼀）袋，填⼟，填⽅12. scrubber洗涤器，涤⽓器，滤清器，板刷，擦布，擦洗者13. incineration 烧尽，焚化，⽕葬14. toxic有毒（性）的，中毒的15. combustible男燃的，可燃的，易激动的16. ramp斜坡，斜⾯，滑⾏台17. excavate挖掘，发掘，在…上挖掘，挖出，变成空洞18. precisely精确的，刻板的，正好，恰恰，确实如此19. aerial空⽓的，⼤⽓的，航空的，架空的，⽣存在空中的20. sonic能发出声⾳的，声⾳的，⾳速的，利⽤⾳波的21. plotting测绘，标图，标航路22. municipal市政的，市⽴的，地⽅⾃治的，地⽅（性）23. commission委任，委托（事项），委员会24. drainage system 排⽔系统Reading Material (1) Careers in Civil EngineeringEngineering is a profession,which means that an engineer must have a specialized university education.many government jurisdictions also have licensing procedures which require engineer graduates to pass an examination,similar to the examination for a lawyer,before they can actively start their careers.In the university,mathematics,physics,and chemistry are heavily emphasized throughout the engineering curricula,but particularly in the first two or three years. Mathematics is very important in all branches of engineering, so it is greatly stressed. Today,mathematics includes courses in statistics, which deals with gathering, classifying, and using numerical data, or pieces of information. An important aspect of statistical mathematics is probability, which deals with what may happen when there are different factors, or variables, that can change the result of a problem. Before the construction of a bridge is undertaken,for example,a statistical study is made of the amount of traffic the bridge will be expected to handle. In the design of the bridge, variable such as water resource on the foundation, impact, the effects of different wind forces and many other factors must be considered.Because a great deal of calculation is involved in solving these problems, computer programming is now included in almost all engineering curricula. Computers, of course, can solve many problems involving calculations with greater speed and accuracy than a human being can do.But computers are useless unless they are given clear and accurate instructions and information,in other words,a good program.In spite of the heavy emphasis on technical subjects in the engineering curricula, a current trend is to require students to take courses in the social science and the language arts. The relationship between engineering and society is getting closer; it is sufficient,therefore,to say again hat the work performed by an engineer affects society in many different and important ways that he or she should be aware of. An engineer also needs a sufficient command of language to be able to prepare reports that are clear and,in many cases,persuasive. An engineer engaged in research will need to be able to write up his or her findings for scientific publications.An engineering program in the last two years includes subjects within the students' field of specialization. For the student who is preparing to become a civil engineer, these specialized courses may concern such subjects as geodetic surveying,soil mechanics,or hydraulics.Active recruiting for engineers often begins before the students?last year in the university.Many different corporation and government agencies have competed for the services of engineers in recent years.In the science-oriented society of today,people who have technical training are ,of course,in demand.Young engineers many choose to go into environmental or sanitary engineering,for example,where environmental concerns have created many openings;or they may choose construction firms that specialized in highway work;or they may prefer to work with one of the government agencies that deal with water resource.In deed,the choice is large and Varied.When a young engineer has finally started actual practice,the theoretical knowledge acquired in the university must be applied.He or she will probably be assigned at the beginning to work with a team of engineers.Thus ,on-the-job training can be acquired that demonstrate his or her ability to translate theory into practice to the supervisors.Civil engineers may work in research, design, construction supervision, maintenance, or even in sales or management. Each of these areas involves different duties, emphases and uses of engineers and also the development and test of newstructural materials.Civil engineering projects are almost always unique; each has its own problems and design features. Therefore, careful study is given to each project even before design work begins. The study includes a survey both of topography and subsoil features of the proposed site. It also includes a consideration of possible alternatives,such as a concrete gravity dam or an earth-fill embankment dam. The economic factors involved in each of the possible alternatives must also be weighed. Today,a study usually includes a consideration of environmental impact of the project. Many engineers,usually working as a team that includes surveyors, specialists in soil mechanics, and experts in design and construction,are involved in making these feasibility studies.Among civil engineers, there are many top people who work in design. As we have seen, civil engineers work on many different kinds of structures,so it is normal practice for an engineer to specialize in just one kind. In designing buildings, engineers often work as consultants in architectural or construction firms. Dams , bridges , water supply systems, and other large projects ordinarily employ several engineers whose work is coordinated by a system engineer who is in charge of the powerhouse and its equipments. In other cases,civil engineers are assigned to work on project in another field; in the space program,for instance, civil engineers are 'necessary in the design and construction of such structures as launching pads and rocket storage facilities.Construction is a complicated process on almost all engineering projects. It involves scheduling the work and utilizing the equipments and the materials so that costs are kept as low as possible. Safety factor must also be taken into account, since construction can be very dangerous.Many civil engineers therefore specialize in the construction phase.Reading Material (2) Civil EngineerA civil engineer is a person who practices civil engineering,the application of planning,designing , constructing, maintaining, and operating infrastructures while protecting the public and environmental health,as well as improving existing infrastructures that have been neglected.Originally, a civil engineer worked on public works projects and was contrasted with a military engineer,who worked on armaments and defenses. Over time, various branches of engineering have become recognized as distinct from civil engineering , including chemical engineering, mechanical engineering,and electrical engineering, while much of miry engineering has been absorbed by civil engineering.In some places, a civil engineer may perform land surveying; in others, surveying is limited to construction surveying,unless an additional qualification is obtained. On some U. S. military bases,the.personnel responsible for buildings and grounds maintenance, such as grass mowing, are called civil .engineers and are not required to meet any minimum educational requirements.SpecializationCivil engineers usually practice in a particular specialty, such as construction engineering,geotechnicalengineering,structural engineering,land development, transportation engineering, hydraulic engineering,and environmental engineering. Some civil engineers, particularly those working for government agencies, may practice across multiple specializations, particularly when involved in critical infrastructure development or maintenance.Education and licensingIn most countries, a civil engineer will have graduated from a post-secondary school with a degree in civil engineering, which requires a strong background in mathematics and physical sciences; this degree is typically a bachelor's degree,though many civil engineers study further to obtain masters,and doctoral degrees. In many countries,civil engineers are subject to licensure. In jurisdictions with mandatory licensing,people who do not obtain a license may not call themselves "civil engineers".EuropeBelgium. In Belgium, Civil Engineer is a legally protected title applicable to graduates of the five-year engineering course in one of the six universities and the Royal Military Academy. Their specialities can be all fields of engineering: civil, structural, electrical, mechanical, chemical, physics and even computer science. This use of the title may cause confusion to English speakers as the Belgian "civil" engineer can have a speciality other than civil engineering. In fact,Belgians use the adjective " civil"as an opposition to military engineers.The formation of the civil engineer has a strong mathematical and scientific base and is more theoretical in approach than the practical oriented industrial engineer educated in a five-year program at a polytechnic. Traditionally, students were required to pass an entrance exam on mathematics to start civil engineering studies. This exam was abolished by the FlemishCommunity in 2004,but is still organized in the French Community.Scandinavia. In Scandinavian countries, a civil engineer is a first professional degree,approximately equivalent to Master of Science in Engineering,and a protected title granted to students by selected institutes of technology. As in English the word has its origin in the distinction between civilian and military engineers,as in before the start of the 19th century only military engineers existed and the prefix "civil" was a way to separate those who had studied engineering in a regular university from their military counterparts. Today the degree spans over all fields within engineering, like civil engineering , computer science , electronics engineering , etc.There is generally a slight difference between a master of science in engineering degree and the Scandinavian civil engineer degree,the latter's program having closer ties with the industry's demands. A civil engineer is the more well-known of the two; still, the area of expertise remains obfuscated for most of the public. A noteworthy difference is the mandatory courses in mathematics and physics , regardless of the equivalent master degree, e. g. computer science.Although a college engineer is roughly equivalent to a bachelor of science in Scandinavia, and to become a civil engineer, one often has had to do up to one extra year of overlapping studies compared to attaining a bachelor of science/master of science combination.This is because the higher educational system is not fully adapted to the international standard graduation system,since it is treated as a professional degree. Today is starts to have a change due to the Bologna process.A Scandinavian "civilingenjor" in international contexts will commonly call herself "master of science in engineering" and will occasionally wear an engineering class ring. At the Norwegian Institute of Technology (now the Norwegian University of Science and Technology) , the tradition with a NTH Ring goes back t0 1914,before the Canadian iron ring.In Norway the title "Sivilingenidr" will no longer be issued after 2007,and has been replaced by "Master of technology". In the English translation of the diploma,the title will be "Master of Science" , since "Master of Technology" is not an established title in the English-speaking world. The extra overlapping year of studies have also been abolished with this change to make Norwegian degrees more equal to their international counterparts.United Kingdom. A chartered civil engineer (known as a certified or professional engineer in other countries) is a member of the Institution of Civil Engineers,and has also passed chartership exams. However, a non-chartered civil engineer may not be a member of the Institution of Civil Engineers or the Institution of Civil Engineering Surveyors. The description "Civil Engineer" is not restricted to members of any particular professional organization although "Chartered Civil Engineer" is .Eastern EuropeIn many Eastern European countries civil engineering does not exist as a distinct degree or profession but its various sub-professions are often studied in separate university faculties and performed as separate professions, whether they are taught in civilian universities or military engineering academies. Even many polytechnic tertiary schools give out separate degrees for each field of study. Typically study in geology,geodesy,structural engineering and urban engineering allows a person to obtain a degree in construction engineeting. Mechanical engineering,automotive engineering , hydraulics and even sometimes metallurgy are fields in a degree of machinery /doc/1d8a7d266137ee06eef91860.html puter sciences,control engineering and electricalengineering are fields in a degree in electrical engineering , while security, safety, environmental engineering, transportation, hydrology and meteorology are in a category of their own, typically each with their own degrees, either in separate university faculties or at polytechnic schools. United StatesIn the United States, civil engineers are typically employed by municipalities, construction firms,consulting engineering firms, architect/engineer firms, state governments, and the federal government. Each state requires engineers who offer their services to the public to be licensed by the state.licensure is obtained by meeting specified education, examination, and work experience the state. Licensure is obtained by meeting spec requirements. Specific requirements vary by state. Typically licensed engineers must graduate from an abet-accredited university or college engine ering program, pass the Fundamentals of Engineering Exam,obtain several years of engineering experience under the supervision of a licensed engineer,and then pass the Principles and Practice of Engineering Exam. After completing these steps and the granting of licensure by a state board,engineers may use the title "Professional Engineer"Building Engineering(建筑⼯程)Ⅰ: Building Types and ComponentsComponents of a BuildingMaterials and structural forms are combined to make up the various parts of a building, including the load-carrying frame, skin, floors, and partitions. The building also has mechanical and electrical systems, such as elevators, heating and cooling systems, and lighting systems. The superstructure is that part of a building above ground, and the substructure and foundation is that part of a building below ground.The skyscraper owes its existence to two developments of the 19th century: steel skeleton construction and the passenger elevator. Steel is a construction material dates from the introduction of the Bessemer converter in 1855. Gustame Eiffel (1832-1923) introduced steel construction in France. His designs for the Galerie des Machines and the Tower for the Paris Exposition of 1889 expressed the lightness of the steel framework. The Eiffel Tower, 984 feet (300 meters) high, was the tallest structure built by man and was not surpassed until 40 years later by a series of American skyscrapers.The first elevator was installed by Elisha Otis in a department store in New York in 1857. In 1889, Eiffel installed the first elevators on a grand scale in the Eiffel Tower, whose hydraulic elevators could transport 2,350 passengers to the summit every hour.Load-carrying frame. Until the late 19th century, the exterior walls of a building were used as bearing walls to support the floors. This construction is essentially a post and lintel type, and it is still used in frame construction for houses. Bearing-wall construction limited the height of buildings because of the enormous wall thickness required; for instance, the 16-story MonadnockBuilding built in the 1880?s in Chicago had walls 5 feet (1.5 meters) thick at the lower floors. In 1883, William Le Baron Jenney (1832-1907) supported floors on cast-iron columns to form a cage-like construction. Skeleton construction, consisting of steel beams and columns, was first used in 1889. As a consequence of skeleton construction, the enclosing walls become a “curtain wall” rather than serving a supporting function. Masonry was the curtain wall mate rial until the 1930?s, when light metal and glass curtain walls were used.After the introduction of the steel skeleton, the height of buildings continued to increase rapidly. All tall buildings were built with a skeleton of steel until World War Ⅱ. After the war, the shortage of steel and the improved quality of concrete led to tall buildings being built of reinforced concrete. Marina Towers (1962) in Chicago is the tallest concrete building in the United States; its height - 588 feet (179 meters) - is exceeded by the 650-foot (198-meter) Post Office Tower in London and by other towers.A change in attitude about skyscraper construction has brought a return to the use of the bearing wall. In New York city, the Columbia Broadcasting System Building, designed by Eero Saarinen in 1962, has a perimeter wall consisting of 5-foot (1.5-meter) wide concrete columns spaced 10 feet (3-meter) from column center to center. This perimeter wall, in effect, constitutes a bearing wall. One reason for this trend is that stiffness against the action of wind can be economically obtained by using the walls of the building as a tube; the World Trade Center buildings are another example of this tube approach. In contrast, rigid frames or vertical trusses are usually provided to give lateral stability.Skin. The skin of a building consists of both transparent elements (windows) and opaque elements (walls). Windows are traditionally glass, although plastics are being used, espeeially in schools where breakage creates a maintenance problem. The wall elements, which are used to cover the structure and are supported by it, are built of a variety of materials: brick precast concrete, stones, opaque glass, plastics, steel, and aluminum. Wood is used mainly in house construction; it is not generally used for commercial, industrial, or public buildings because of the fire hazard.Floors. The construction of the floors in a building depends on the basic structural frame that is used. In steel skeleton construction, floors are either slabs of concrete resting on steel beams or a deck consisting of corrugated steel with a concrete topping. In concrete construction, the floors are either slabs of concrete on concrete beams or a series of closely spaced concrete beams (ribs) in two directions topped with a thin concrete slab, giving the appearance of a waffle on its underside. The kind of floor that is used depends on the span between supporting columns or walls and function of the space. In an apartment building, for instance, where walls and columns are spaced at 12 to 18 feet (3.7 to 5.5 meters), the most popular construction is a solid concrete slab with no beams. The underside of the slab serves as the ceiling for the space below it. Corrugated steel decks are often used in office buildings because the corrugations, when enclosed by another sheet of meta1, form ducts for telephone and electrical lines.Mechanical and Electrical Systems. A modern building not only contains the space for which it is intended (office, classroom, apartment) but also contains ancillary space for mechanical and electrical systems that help to provide a comfortable environment. These ancillary spaces in a skyscraper office building may constitute 25% of the total building area. The importance of heating, ventilating, electrical, and plumbing systems in an office building is shown by the fact that 40% of the construction budget is allocated to them. Because of the increased use of sealedbuildings with windows that cannot be opened, elaborate mechanical systems are provided for ventilation and air conditioning. Ducts and pipes carry fresh air from central fan rooms and air conditioning machinery. The ceiling, which is suspended below the upper floor construction, conceals the ductwork and contains the lighting units. Electrical wiring for power and for telephone communication may also be located in this ceiling space or may be buried in the floor construction in pipes or conduits.There have been attempts to incorporate the mechanical and electrical systems into the architecture of buildings by frankly expressing them; for example, the American Republic Insurance Company Building (1965) in Des Moines, Iowa, exposesboth the ducts and the floor structure in an organized and elegant pattern and dispenses with the suspended ceiling. This type of approach makes it possible to reduce the cost of the building and permits innovations, such as in the span of the structure.Soil and Foundations. All buildings are supported on the ground, and therefore the nature of the soil becomes an extremely important consideration in the design of any building. The design of a foundation depends on many soil factors, such as type of soil, soil stratification, thickness of soil layers and their compaction, and groundwater conditions. Soils rarely have a single composition; they generally are mixtures in layers of varying thickness. For evaluation, soils are graded according to particle size, which increases from silt to clay to sand to gravel to rock. In general, the larger particle soils will support heavier loads than the smaller ones. The hardest rock can support loads up to 100 tons per square foot (976.5 metric tons/sq meter), but the softest silt can support a load of only 0.25 ton per square foot (2.44 metric tons/sq meter). All soils beneath the surface are in a state of compaction; that is, they are under a pressure that is equal to the weight of the soil column above it. Many soils (except for most sands and gavels) exhibit elastic properties - they deform when compressed under load and rebound when the load is removed. The elasticity of soils is of - ten time - dependent, that is, deformations of the soil occur over a length of time, which may from minutes to years after a load is 1m - posed. Over a period of time, a building may settle if it imposes a load on the soil greater than the natural compaction weight of the soil. Conversely, a building may heave if it imposes loads on the soil smaller than the natural compaction weight. The soil may also flow under the weight of a building; that is, it tends to be squeezed out.Due to both the compaction and flow effects, buildings tend to settle. Uneven settlements, exemplified by the leaning towers in Pisa and Bologna, can have damaging effects - the building may lean, walls and partitions may drack, windows and doors may become inoperative, and in the extreme, a building may collapse. Uniform settlements are not so serious, although extreme conditions, such as those in Mexico City, can have serious consequences. Over the past 100 years, a change in the groundwater level there has caused some buildings to settle more than 10 feet (3 meters). Because such movements can occur during and after construction, careful analysis of the soils under a building is vital.The great variability of soils has led to a variety of solutions to the foundation problem. Where firm soil exists close to the surface, the simplest solution is to rest columns on a small slab of concrete (spread footing). Where the soil is softer, it is necessary to spread the column load over a greater area; in this case, a continuous slab of concrete (raft or mat) under the whole building is used. In cases where the soil near the surface is unable to support the weight of the building, piles of wood or concrete are driven down to firm soil.The construction of a building proceeds naturally from the foundation up to the superstructure. The design process, however, proceeds from the roof down to the foundation (in the direction of gravity). In the past, the foundation was not subjected to systematic investigation. A scientific approach to the design of foundations has been developed in the 20th century. Karl Terzaghi of the United States pioneered studies that made it possible to make accurate predictions of the behavior of foundations, using the science of soil mechanics coupled with exploration and testing procedures. Foundation failures of the past, such as the classical example of the leaning tower in Pisa, have become almost nonexistent. Foundations still are a hidden but costly part of many Buildings.New Words and Expressions1.partition [ pɑ:'ti??n ] n. 分开，分割，隔墙，隔板2.converter [ k?n'v?:t? ] n. 炼钢炉，吹风转炉3.framework [ 'freimw?:k ] n. 构架，框架，结构4.surpass [ s?'pɑ:s ] v. 超过，胜过5.exterior [ ik'sti?ri? ] adj. 外部的，外⾯的n. 外部，表⾯6.lintel [ 'lint?l ] n. 楣，（门窗）过梁7.opaque [ ?u'peik ] adj. 透明的，不透光的n. 不透明体8.deck [ dek ] n. 甲板，舱⾯；桥⾯，层⾯9.corrugate [ 'k?:ruɡeit ] v. 弄皱，使起皱纹adj. 起皱的，起波纹的10.duct [ d?kt ] n. 管道，通道，预应⼒筋孔道11.ancillary [ ?n'sil?ri ] adj. 辅助的，附属的12.ventilate [ 'ventileit ] vt. 使通风，使通⽓，给……装置通风设备。
非广延统计力学中的理查逊公式非广延统计力学（nonextensivestatisticalmechanics）是新兴的物理学理论，由美国物理学家布列松在1995年发表。
它是基于质点系统的分布函数通过定义一个一般性参数来描述一个较大系统。
它是传统统计力学的改进，它增加了它的适用性，可以改善在复杂系统中经典统计力学的失败。
在非广延统计力学的基础上，物理学家理查逊提出了一个重要的理论--理查逊公式，它为系统的宏观性质提供了描述。
理查逊公式由一个表达熵的参数组成，它是描述一个物理系统的概率分布函数的基本参数之一，主要用于描述一个或多个状态变量的热力学特性。
理查逊公式的熵的表达式为：S = klnW其中S为熵，K为玻尔兹曼常数，ln为自然对数，W表示概率分布函数的参数。
理查逊公式的特点是按照某种规律的概率分布函数，可以简化熵的计算。
它的优点在于可以节省计算时间，节省计算资源，减少计算过程中的误差。
理查逊公式对非广延统计力学有重要意义，用于计算熵，可以更容易、更快速地描述一个系统，并且可以更容易地描述有关系统宏观性质和参数之间的关系。
因此，理查逊公式可以用于应用于描述复杂系统中的宏观性质，例如把物理系统的分布函数映射到它的宏观性质上来描述。
理查逊公式的应用广泛，它可以用于描述广义平衡态系统的宏观性质，即自由能的分布函数，用于计算被系统中的概率分布函数的影响程度。
另外，它也可以应用于复杂系统的分析，包括量子系统和核物理中的系统分析以及原子核和物质性质的研究。
此外，它也可以应用于体系和动力学分析中，用于描述平衡态和动力学过程。
总之，理查逊公式是非广延统计力学中一项重要的理论，它的应用非常重要，几乎可以运用到所有的物理学领域中，它有助于更好地描述复杂系统的宏观性质，准确获取它们的参数和熵，从而提供一种有效的分析方法。
专业英语八级（阅读）练习试卷20(题后含答案及解析) 题型有： 2. READING COMPREHENSIONPART II READING COMPREHENSION (30 MIN)Directions: In this section there are four reading passages followed by a total of 20 multiple-choice questions. For each of them there are four choices marked A, B, C and D. You should decide on the best choice.Lately, everybody from industrial designers to city planners claims to be looking after our aesthetic interests, and there is ample anecdotal evidence that, on the margin, people do put a higher premium on the look and feel of things than they once did. That is to be expected as society grows richer. But aesthetics is not the only value -- trade-offs must be made -- and aesthetic value is hard to measure. What is “it,” after all? Aesthetics doesn’t come in neat units like microprocessor speed, calories, or tons of steel. Style is qualitative. The value of qualitative improvements poses tricky problems for economists. It is a major challenge to tease out how much consumers value each individual attribute that comes bundled in a given good or service. If you pay $2.99 for a toothbrush, how much of that is for the cleaning ability? How much for the feel of the handle? How much for the durability? How much for the packaging? How much for the convenient distribution to your comer drugstore? How much for the color? Economists use statistical techniques called “hedonic pricing” to try to separate the implicit prices of various characteristics. Essentially, they look at how prices go up or down as features are added or subtracted and try to figure out how consumers value the individual features. How much will consumers pay for an extra megahertz of computing speed, for instance? Not every characteristic is as easily measured as megahertz. The trickier the measurement, the more difficult the problem. For aesthetics, economists generally don’t even try. It’s just too hard. How do you account for the restaurant d écor or subtle enhancements in the taste of the food? How do you measure the increased value of a typeset resume, memo or client newsletter -- the result of ubiquitous word processors -- over an old-fashioned typed document? That sort of detail is simply lost in crude economic statistics. Many product characteristics -- from convenience to snob appeal to aesthetics -- are hard to quantify and so tend to be undercounted. The result is that the standard of living can change for the better without much notice. That is especially likely if products improve without becoming more expensive. Consumers are happier, but if they aren’t spending more money, no revenue increase shows up in the productivity statistics. This isn’t unusual in competitive markets. Shopping malls redecorate, and newspapers adopt color printing just to keep up with the competition. They aren’t able to charge more. They are just able to stay in business. When thinking about new products, producers face two challenges. First, they need to offer something whose value to the consumer is greater than its cost to produce and distribute. Increasing the surplus ofvalue minus cost is where both higher living standards and higher profits come from. It is the measure of real economic improvement. The second challenge is, of course, to price the offering to maximize profit. As a general matter, aesthetics sells. But “as a general matter” obscures all the specifics that make or break a product: What exact design will you use? How will you manufacture it? What will you charge? And, given those decisions, how will customers respond? The answers can’t be found through a blackboard exercise. Price theory is a useful tool, but we can’t know in advance how much people will value the characteristics of a product they haven’t yet seen or compared with real alternatives. Even market research, while helpful, cannot duplicate real-life choices. Although we all have fun predicting and second-guessing business ideas, the only way to find out is through trial and error. Market competition is a discovery process that subjects business hypotheses to unsentimental testing. Some managers are better than others at identifying promising new sources of value, and some companies are better than others at operations and pricing -- the skills that determine whether a product that consumers do value will in fact be profitable. Market competition tests these theories and skills. And, like all competitions, this one has its failures, some of them beautiful. Not every attempt at improvement works out. Sometimes value does not exceed cost. Sometimes it does, but managers fall in love with their product, price it too high and drive away potential customers. Sometimes the coolest of the cool just can’t survive the heat. With 20/20 hindsight, it is easy to see that the pricey Cube was doomed. But nobody knew that a year ago.1．The passage is mainly concerned with ______.A．adding aesthetics to productsB．increasing surplus of value minus costC．quantifying product characteristicsD．putting business ideas to market testing正确答案：C解析：本文主要讨论了如何对产品的抽象属性进行价格定位这一问题。
Statistical mechanics or statistical thermodynamics[note 1] is a branch of physics that applies probability theory, which contains mathematical tools for dealing with large populations, to the study of the thermodynamic behavior of systems composed of a large number of particles. Statistical mechanics provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a result of classical and quantum-mechanical description of statistics and mechanics at the microscopic level.Statistical mechanics provides a molecular-level interpretation of macroscopic thermodynamic quantities such as work, heat, free energy, and entropy. It enables the thermodynamic properties of bulk materials to be related to the spectroscopic data of individual molecules. This ability to make macroscopic predictions based on microscopic properties is the main advantage of statistical mechanics over classical thermodynamics. Both theories are governed by the second law of thermodynamics through the medium of entropy. However, entropy in thermodynamics can only be known empirically经验得, whereas in statistical mechanics, it is a function of the distribution of the system on its micro-states.Statistical mechanics was initiated in 1870 with the work of Austrian physicist Ludwig Boltzmann, much of which was collectively published in Boltzmann's 1896 Lectures on Gas Theory.[1] Boltzmann's original papers on the statistical interpretation of thermodynamics, the H-theorem, transport theory, thermal equilibrium, the equation of state of gases, and similar subjects, occupy about 2,000 pages in the proceedings of the Vienna Academy and other societies. The term "statistical thermodynamics" was proposed for use by the American thermodynamicist and physical chemist J. Willard Gibbs in 1902. According to Gibbs, the term "statistical", in the context of mechanics, i.e. statistical mechanics, was first used by the Scottish physicist James Clerk Maxwell in 1871. "Probabilistic mechanics" might today seem a more appropriate term, but "statistical mechanics" is firmly entrenched.[2]Overview The essential problem in statistical thermodynamics is to calculate the distribution of a given amount of energy E over N identical systems.[3] The goal of statistical thermodynamics is to understand and to interpret the measurable macroscopic properties of materials in terms of the properties of their constituent particles and the interactions between them. This is done by connecting thermodynamic functions to quantum-mechanic equations. Two central quantities in statistical thermodynamics are the Boltzmann factor and the partition functionLastly, and most importantly, the formal definition of entropy of a thermodynamic system from a statistical perspective is called statistical entropy, and is defined as:wherekB is Boltzmann's constant 1.38066×10−23 J K−1 andis the number of microstates corresponding to the observed thermodynamic macrostate. This equation is valid only if each microstate is equally accessible (each microstate has an equal probability of occurring).Boltzmann distributionIf the system is large the Boltzmann distribution could be used (the Boltzmann distribution is an approximate result)This can now be used with :Fundamental postulateThe fundamental postulate in statistical mechanics (also known as the equal a priori probability postulate) is the following:Given an isolated system in equilibrium, it is found with equal probability in each of its accessible microstates.This postulate is a fundamental assumption in statistical mechanics - it states that a system in equilibrium does not have any preference for any of its available microstates. Given Ω microstates at a particular energy, the probability of finding the system in a particular microstate is p = 1/Ω. This postulate is necessary because it allows one to conclude that for a system at equilibrium, the thermodynamic state (macrostate) which could result from the largest number of microstates is also the most probable macrostate of the system.The postulate is justified in part, for classical systems, by Liouville's theorem (Hamiltonian), which shows that if the distribution of system points through accessible phase space is uniform at some time, it remains so at later times.Similar justification for a discrete system is provided by the mechanism of detailed balance.This allows for the definition of the information function (in the context of information theory):When all the probabilities (ρi) are equal, I is maximal, and we have minimal information about the system. When our information is maximal (i.e., one rho is equal to one and the rest to zero, such that we know what state the system is in), the function is minimal.This information function is the same as the reduced entropic function in thermodynamics.Statistical ensemblesThe modern formulation of statistical mechanics is based on the description of the physical system by an ensemble that represents all possible configurations of the system and the probability of realizing each configuration.Each ensemble is associated with a partition function that, with mathematical manipulation, can be used to extract values of thermodynamic properties of the system. According to the relationship of the system to the rest of the universe, one of three general types of ensembles may apply, in order of increasing complexity:Microcanonical ensemble: describes a completely isolated system, having constant energy, as it does not exchange energy or mass with the rest of the universe.Canonical community: describes a system in thermal equilibrium with its environment. It may only exchange energy in the form of heat with the outside.Canonical partitionfunctionGrand canonical partition functionThermodynamic connectionThe partition function can be used to find the expected (average) value of any microscopic property of the system, which can then be related to macroscopic variables. For instance, the expected value of the microscopic energy E is interpreted as the microscopic definition of the thermodynamic variable internal energy U, and can be obtained by taking the derivative of the partition function with respect to the temperature. Indeed,implies, together with the interpretation of as U, the following microscopic definition of internal energy:The entropy can be calculated by (see Shannon entropy)which implies thatis the free energy of the system or in other words,Having microscopic expressions for the basic thermodynamic potentials U (internal energy), S (entropy) and F (free energy) is sufficient to derive expressions for other thermodynamic quantities. The basic strategy is as follows. There may be an intensive or extensive quantity that enters explicitly in the expression for the microscopic energy Ei, for instance magnetic field (intensive) or volume (extensive). Then, the conjugate thermodynamic variables are derivatives of the internal energy. The macroscopic magnetization (extensive) is the derivative of U with respect to the (intensive) magnetic field, and the pressure (intensive) is the derivative of U with respect to volume (extensive).The treatment in this section assumes no exchange of matter (i.e. fixed mass and fixed particle numbers). However, the volume of the system is variable which means the density is also variable.This probability can be used to find the average value, which corresponds to the macroscopic value, of any property, J, that depends on the energetic state of the system by using the formula:where is the average value of property J. This equation can be applied to the internal energy,U:Subsequently, these equations can be combined with known thermodynamic relationships between U and V to arrive at an expression for pressure in terms of only temperature, volume and the partition function. Similar relationships in terms of the partition function can be derived for other thermodynamic properties as shown in the following table; see also the detailed explanation in configuration integral.Helmholtz free energy:Internal energy:Pressure:Entropy:Gibbs free energy:Enthalpy:Constant volume heat capacity:Constant pressure heat capacity:Chemical potential:Classical thermodynamics vs. statistical thermodynamics As an example, from a classical thermodynamics point of view one might ask what is it about a thermodynamic system of gas molecules, such as ammonia NH3, that determines the free energy characteristic of that compound? Classical thermodynamics does not provide the answer. If, for example, we were given spectroscopic data, of this body of gas molecules, such as bond length, bond angle, bond rotation, and flexibility of the bonds in NH3 we should see that the free energy could not be other than it is. To prove this true, we need to bridge the gap between the microscopic realm of atoms and molecules and the macroscopic realm of classical thermodynamics. From physics, statistical mechanics provides such a bridge by teaching us how to conceive of a thermodynamic system as an assembly of units. More specifically, it demonstrates how the thermodynamic parameters of a system, such as temperature and pressure, are interpretable in terms of the parameters descriptive of such constituent atoms and molecules.[6]In a bounded system, the crucial characteristic of these microscopic units is that their energies are quantized. That is, where the energies accessible to a macroscopic system form a virtual continuum of possibilities, the energies open to any of its submicroscopic components are limited to a discontinuous set of alternatives associated with integral values of some quantum number.。
a r X i v :n u c l -t h /9902070v 2 14 O c t 1999Nonextensive statistics,fluctuations and correlations in high energy nuclear collisions∗W.M.Alberico 1,3,vagno 2,3and P.Quarati 2,41Dipartimento di Fisica,Universit`a di Torino,Via P.Giuria 1,I-10124Torino,Italy2Dipartimento di Fisica,Politecnico di Torino,C.so Duca degli Abruzzi 24,I-10129Torino,Italy3Istituto Nazionale di Fisica Nucleare,Sezione di Torino4Istituto Nazionale di Fisica Nucleare,Sezione di Cagliari Starting from the experimental evidence that high–energy nucleus–nucleus collisions cannot be described in terms of superpositions of elementary nucleon–nucleon interactions,we analyze the possibility that memory effects and long–range forces imply a nonextensive statistical regime during high energy heavy ion collisions.The relevance of these statistical effects and their compatibility with the available experimental data are discussed.In particular we show that theoretical estimates,obtained in the framework of the generalized nonextensive thermostatistics,can reproduce the shape of the pion transverse mass spectrum and explain the different physical origin of the transverse momentum correlation function of the pions emitted during the central Pb+Pb and during the p+p collisions at 158A GeV.I.INTRODUCTION In the last years,many efforts have been focussed on the study of high energy nuclear collisions,resulting in a better understanding of the strongly interacting matter at high energy rge acceptance detectors provide a detailed analysis of the multiplicity of produced particles;this in turn can be related to possible signatures of the formation of a new phase of matter,the so–called quark–gluon plasma (QGP),in the early stages of high energy heavy ion collisions [1].One of the most interesting experimental results is that high energy nucleus–nucleus (A+A)collisions cannot be described in terms of superpositions of elementary nucleon–nucleon (N+N)interactions (proton–proton or proton–antiproton).The different conditions of energy density and temperature at the early stage of the Pb+Pb and of the p+p collisions (to mention just two extreme examples)generate collective effects that modify the features of freeze–out observables.Of course the most appealing explanation would be to interpret the presence of these evident experimental differences as an indirect consequence of the formation of QGP in the early stages of heavy ion collisions.It is an experimentally established fact [2]that the slope parameter of the transverse momentum distribution significantly increases with the particle mass when going from p+p to central Pb+Pb collisions.On the other hand,the preliminary results of the NA49Collaboration [3,4]indicate that the transverse momentum fluctuations in central Pb+Pb collisions at 158A GeV have a quite different physical origin with respect to the corresponding fluctuations in p+p collisions.Let us also recall that the observed J/Ψsuppression increases continuously and monotonically from the lightest (p+p)to the heaviest (S+U)interacting nuclei,but it exhibits a clear departure from this ”normal”behavior for central Pb+Pb collisions [5].These experimental features have been explained in terms of collective effects in the hadronic medium (such as the presence of a transverse hydrodynamical expansion)and considering the strong influence of secondary rescatterings in heavy ion collisions [2,6–8].It is a very important issue to understand whether the system is able to reach full thermalization;up to now this question has been the subject of many experimental and theoretical studies.However several experimental observables,such as transverse mass spectrum,multiplicity of particles,three–dimensional phase–space density of pions,are well reproduced in the framework of local thermal equilibrium in a hydrodynamical expanding environment [8–12].In this paper we start from the hypothesis that memory effects and long–range forces can occur during high energy heavy ion collisions:in this case the strong influence of collective effects on the experimental observables can be understood in a very natural way in the framework of the generalized nonextensive thermostatistics.In this context we show that the transverse momentum correlations of the pions emitted from central Pb+Pb collisions can be very well reproduced by means of very small deviations from the standard equilibrium extensive statistics.In Sec.II we summarize the main assumptions contained in the derivation of the dynamical kinetical equations and their relevance to the determination of the equilibrium phase–space distribution.In Sec.III we examine whether theseconditions are met in the high energy heavy ion collisions and which experimental observables can be sensitive to the presence of nonextensive statistical effects.In Sec.IV we introduce the nonextensive Tsallis thermostatistics which isconsidered the natural generalization of the standard classical and quantum statistics when memory effects and/or long range forces are not negligible.In Sec.V we show how the generalized distribution function modifies the shape of the transverse mass spectrum and in Sec.VI we investigate the influence of nonextensive particlefluctuations in thedetermination of the measure of the transverse momentum correlations.Finally,a discussion of the results and some conclusions are reported in Sec.VII.II.DYNAMICAL KINETICAL APPROACH TO THERMAL EQUILIBRIUM AND EXTENSIVESTATISTICSAssuming local thermal equilibrium,the freeze–out observables are usually calculated within the extensive thermo-statistics.In particular,the equilibrium transverse momentum distribution is assumed to be,in the classical case,the standard Maxwell–Boltzmann(J¨u ttern)distribution.If the emitted particles are light enough,such as pions,to havenoticeable quantum degeneracy,one must use the Bose–Einstein(or Fermi–Dirac,for fermions)distribution.When the system approaches equilibrium,the phase–space distribution should be derived as a stationary state ofthe dynamical kinetical evolution equation.If,for sake of simplicity,we limit our discussion to the classical case,the Maxwellian distribution is obtained as a steady state solution of the Boltzmann equation.Let us now briefly review the principal assumptions in the derivation of the Boltzmann equation and examine how these approximations canaffect the determination of the equilibrium distribution[13].One important assumption concerns the collision time, which must be much smaller than the mean time between collisions.This request can be expressed by the condition nr30≪1,where n is the density and r0is the effective range of the interactions.This condition has two important physical consequences.a)There is no overlapping between subsequent collisions involving a given particle and the interactions can be described as a succession of simple binary collisions.b)It is always possible to define a timeinterval in which the single particle distribution does not change appreciably and its rate of change at time t depends only on its instantaneous value and not on its previous history.Hence this property reflects the Markovian character of the Boltzmann equation:no memory is taken into account.The second assumption is analoguous to thefirst one,but for the space dependence of the distribution function: its rate of change at a spatial point depends only on the neighborhood of that point.In other words the range of the interactions is short with respect to the characteristic spatial dimension of the system.The last important assumption is the so–called Bolzmann’s Stosszahlansatz:the momenta of two particles at the same spatial point are not correlated and the corresponding two body correlation function can be factorized as a product of two single particle distributions.This assumption is very important because it allows us to write down the collisional integral(which is equal to the total time rate of change of the distribution function)in terms of the single particle distribution only.The above assumptions,namely the absence of non–Markovian memory effects,the absence of long–range interactions and negligible local correlations,together with the Boltzmann’s H theorem(based on the extensive definition of the entropy)lead us to the well–known stationary Maxwellian distribution.The basic assumption of standard statistical mechanics is that the system under consideration can be subdividedinto a set of non–overlapping subsystems.As a consequence the Boltzmann–Gibbs entropy is extensive in the sense that the total entropy of two independent subsystems is the sum of their entropies.If memory effects and long range forces are present,this property is no longer valid and the entropy,which is a measure of the information about the particle distribution in the states available to the system,is not an extensive quantity.In the next section,we will see whether the above assumptions are implemented during high energy nuclear collisionsand if there appear experimental signals that can be interpreted as a consequence of the presence of a nonextensive regime.III.DO HEA VY ION COLLISIONS SATISFY EXTENSIVE STATISTICS?It is a rather common opinion that,because of the extreme conditions of density and temperature in ultrarelativistic heavy ion collisions,memory effects and long–range color interactions give rise to the presence of non–Markovian processes in the kinetic equation affecting the thermalization process toward equilibrium as well as the standard equilibrium distribution[14–17].A rigorous determination of the conditions that produce a nonextensive behavior,due to memory effects and/or long–range interactions,should be based on microscopic calculations relative to the parton plasma originated during the high energy collisions.At this stage we limit ourselves to consider the problem from a qualitative point of view on the basis of the existing theoretical calculations and experimental evidences.Under the hypothesis that QGP is generated in the high energy collisions,the quantities characterizing the plasma,such as lifetime and damping rates of quasiparticles,are usually calculated within finite temperature perturbative QCD.This approach is warranted by the fact that at high temperature (beyond a few hundred MeV)the strong QCD coupling αs =g 2/4πbecomes very small and “weak coupling”regime takes place.In this regime (g ≪1)the longitudinal gluon propagator is characterized by a Debye mass m D ≈gT ,and the corresponding screening length (λD =m −1D ≈1/gT )is much larger than the mean interparticle distance ( r ≈n −1/3≈1/T )(for a review,see e.g.,Ref.[18]).Therefore a great parton number is contained in the Debye sphere and the ordinary mean field approximation of QGP (Debye–H¨u ckel theory)holds.Nevertheless,in the proximity of the phase transition,the QGP is no longer a system of weakly interacting particles and non–perturbative QCD calculations become important.Recently it has been shown [19]that for temperature near the critical one (T ≥1.1T c )non–perturbative calculations imply an effective quark mass very close to T ,sensibly different from the value,proportional to gT ,obtained in perturbative regime.Near the phase transition the characteristic quantity nr 30≈nλ3D should then be very close to one and only a small number of partons is present in the Debye sphere:the ordinary mean field approximation of the plasma is no longer correct and memory effects are not negligible.In addition,we observe that in high density quark matter the color magnetic field remains unscreened (in leading order)and long–range color magnetic interaction should be present at all temperatures.From the above considerations it appears reasonable that,if the deconfining phase transition takes place,non–Markovian effects and long range interactions can influence the dynamical evolution of the generated fireball toward the freeze–out stage.Moreover they will affect the equilibrium phase–space distribution function if thermal equilibrium is attained.A signature of these effects should show up in physical observables.In this context,we notice that the authors of Ref.[7]raise a controversy on the Markovian description of the multiple scattering processes,one of the assumptions of the UrQMD model.This example concerns (e +e −→µ+µ−)scattering,where a determination of the angular distribution based on the Markovian approximation of the transport theory leads to wrong results [20,21,17].The aim of the present work is to suggest a possible interpretation of the above mentioned difference between the correlactions/fluctuations of the pion transverse momentum measured in p+p and Pb+Pb collisions [11]as a signature of the nonextensivity of the system.In fact,it has been shown [22]that,whether the equilibrium condition is realized or not,the measure of the correlations/fluctuations strongly depends on the factorization of the multiparticle distributions and on the event by event multiplicity of the particles under consideration.Such property implies that the (multi)particle distribution functions are not inclusive (the distribution functions of one,two,or more bodies,depend on the presence of the other particles of the system).In turn,this is a manifestation of a nonextensive behavior of the system.In addition we notice that,from a recent analysis of the average pion phase–space density at freeze–out in S–nucleus and Pb–Pb collisions at SPS,the experimental data indicate a slower decrease with increasing p ⊥than the Bose–Einstein curve [23].The analysis of the same quantity in π–p collisions seems,instead,to be consistent with the standard expectations.We remind that in Ref.[24]the authors show that by assuming the standard J¨u ttern momentum distribution of emitted particles in high energy collisions one is led to unrealistic consequences and the physical freeze–out is actually not realized.From the foregoing considerations we conclude that both theoretical calculations and experimental observables agree with the existence of nonextensive features in high energy heavy ion collisions.IV.GENERALIZED NONEXTENSIVE TSALLIS STATISTICSSeveral new developments in statistical mechanics have shown that in the presence of long–range forces and/or in irreversible processes related to microscopic long–time memory effects,the extensive thermodynamics,based on the conventional Boltzmann–Gibbs thermostatistics,is no longer correct and,consequently,the equilibrium particle distribution functions can show different shapes from the conventional well known distributions.Standard sums,or integrals,which appear in the calculation of thermostatistical quantities,like the partition function,the entropy,the internal energy,etc.can diverge.These difficulties are well known in several physical domains [25]since long time.A quite interesting generalization of the conventional Boltzmann–Gibbs statistics has been recently proposed by Tsallis [26]and proves to be able to overcome the shortcomings of the conventional statistical mechanics in manyphysical problems,where the presence of long–range interactions,long–range microscopic memory,or fractal space–time constraints hinders the usual statistical assumptions.Among other applications,we quote astrophysical self–gravitating systems[27],the solar neutrino problem[28],cosmology[29],many–body,dynamical linear response theory and variational methods[30],phase shift analyses for the pion–nucleus scattering[31].The Tsallis generalized thermostatistics is based upon the following generalization of the entropy[26]1S q=[1+(q−1)β(E i−µ)]1/(q−1)±1,(4) where the+sign is for fermions,the−for bosons andβ=1/T.In the limit q→1(extensive statistics),one recovers the conventional Fermi–Dirac and Bose–Einstein distribution.Let us remind that the Tsallis generalized statistics does not entail a violation of the Pauli exclusion principle and does not modify the inclusive behavior of the bosons,but it modifies,with the generalized nonextensive entropy (1),the extensive nature of the standard statistics.At the equilibrium,the nonextensive statistics implies afinite temperature particle distribution different from the standard Fermi–Dirac and Bose–Einstein distributions;in the classical limit,one has the following generalized Maxwell–Boltzmann distribution[26]:n i q=[1+(q−1)β(E i−µ)]1/(1−q).(5) When the entropic q parameter is smaller than1,the distributions(4)and(5)have a natural high energy cut–off: E i≤1/[β(1−q)]+µ,which implies that the energy tail is depleted;when q is greater than1,the cut–offis absent and the energy tail of the particle distribution(for fermions and bosons)is enhanced.Hence the nonextensive statistics entails a sensible difference of the particle distribution shape in the high energy region with respect to the standard statistics.This property plays an important rˆo le in the interpretation of the physical observables,as it will be shown in the following.V.TRANSVERSE MASS SPECTRUM AND Q–BLUE SHIFTThe applicability of the equilibrium statistical mechanics relies on the recognition that the experimental transverse mass spectrum and the relative abundance of charged particles(pions,kaons,protons,etc.)can be described within the equilibrium formalism.The single particle spectrum can be expressed as an integral over a freeze–out hypersurface Σf[33]E d3Ndy m⊥dm⊥dφ=gm⊥dm⊥=A m⊥K1(z),(7)where z=m⊥/T and K1is thefirst order modified Bessel function.In the asymptotic limit,m⊥≫T(z≫1),the above expression gives rise to the exponential shapedNm⊥e−z,(8)which is usually employed tofit the experimental transverse mass spectra and provides an indication of a thermal energy distribution.Although,from a general perspective,the experimental distribution of particle momenta in the transverse direction is described by an exponentially decreasing behavior,at higher energies the experimental data deviate from the usual Boltzmann slope.This discrepancy can be cured by introducing the dynamical effect of a collective transverseflow which predicts the so–called blue shift factor,i.e.,an increase of the slope parameter T at large m⊥.The experimental slope parameter measures the particle energy,which contains both thermal(random)and col-lective(mainly due to rescattering)contributions.The thermal motion determines the freeze–out temperature T fo, namely the temperature when particles cease to interact with each other.In the presence of a collective transverse flow[2]one can extract T fo from the empirical relationT=T fo+m v⊥ 2,(9) where v⊥ is afit parameter which can be identified with the average collectiveflow velocity;the latter is consistent with zero in p+p reactions,but can be large in collisions between heavy nuclei(where rescattering is expected to be important).In Eq.(9),m is the mass of the detected particle(e.g.pions,kaons,protons).Let us consider a different point of view and argue that the deviation from the Boltzmann slope at high p⊥can be ascribed to the presence of nonextensive statistical effects in the steady state distribution of the particle gas;the latter do not exclude the physical effect of a collectiveflow but rather incorporates a description of it from a slightly different statistical mechanics analysis.If long tail time memory and long–range interactions are present,as already discussed in Sec.III,the Maxwell–Boltzmann distribution must be replaced by the generalized distribution(5).We consider here only small deviations from standard statistics(q−1≈0);then atfirst order in(q−1)the transverse mass spectrum can be written asdN8z2[3K1(z)+K3(z)] ,(10)where K3is the modified Bessel function of the third order.In the asymptotic limit,z≫1(but always for q values close to1,such that(q−1)z≪1),we obtain the following generalization of Eq.(8):dNm⊥exp −z+q−1T q=T+(q−1)m⊥.(12) Hence nonextensive statistics predicts,in a purely thermal source,a generalized q–blue shift factor at high m⊥; moreover this shift factor is not constant but increases(if q>1)with m⊥=Z2xx is a single particle variable and Z x= N i=1(x i−ρ d3p p⊥ 2 n q,(14) andZ2p⊥ρ d3p p⊥ 2 ∆n2 q,(15) where the quantityp⊥=1(2π)3p⊥ n q withρ= d3pβ∂ n q1+(q−1)β(E−µ)(1∓ n q),(17)where E is the relativistic energy E=∆n2,which,for the ideal Fermi–Dirac(Bose–Einstein)gas,are suppressed(enhanced)with respect to the classical case.In the nonextensive Tsallis statistics,thefluctuations of an ideal gas of fermions(bosons),expressed by Eq.(17),are still suppressed(enhanced)by the factor1∓ n q;this effect,however,is modulated by the factor[1+(q−1)β(E−µ)]−1in the right hand side of Eq.(17).Therefore thefluctuations turn out to beincreased for q<1(we remind that due to the energy cut–offcondition the above factor is always positive)and are decreased for q>1.The measureΦdoes not have,both for bosons and fermions,a constant sign and it is positiveor negative depending on the value of the entropic parameter q.In the classical nonextensive case we also have∆n2 q= n q.The quantity ∆n2 q is greater than n q for q<1,and smaller for q>1and the correlation measure Φcan be different from zero for q=1.This is essentially due to the intrinsic nature of the system in the presenceof memory effects and/or long–range forces and to the dependence of the(multi)particle distribution functions uponthe surrounding medium.We use Eqs.(14)and(15)to evaluate the correlation measureΦp⊥for the pion gas(mπ=140MeV),which we cancompare with the experimental results measured in the central Pb+Pb collision by the NA49collaboration[3,4].Letus notice that the values ofΦp⊥,which depends on T,µand the entropic parameter q,are very sensitive to smallvariations of q.This is mainly due to the modified expression(17)of thefluctuations in the nonextensive statistics.In Fig.1we showΦp⊥as a function of the parameter q,at different(fixed)values of the temperature and chemicalpotential.The experimental data are reported up to a maximum value of the transverse momentum p⊥=1.5GeV: hence we have limited the integration up to the upper limit of1.5GeV.Concerning the temperature T,we use the slope parameter derived from thefit of the transverse momentum spectra[2,39].With T=170MeV andµ=60MeV(according to the suggestion of[40]),we obtainΦp⊥=5MeV with q=1.038,while the usual extensive statistics,with q=1,givesΦp⊥=24.7MeV(we remind that a non–vanishing value ofµimplies that there is no chemicalequilibrium).By choosingµ=0MeV one can obtain the same valueΦp⊥=5MeV with a smaller q(q=1.015).In this case,with q=1,Φp⊥=13.6MeV.Thus,a very little deviation from the standard Bose–Einstein distribution is sufficient to obtain theoretical estimates in agreement with the experimental results.We notice also that the value employed,q≈1,justifies,a posteriori,the approximation of the analytical form of the distribution function(4)and the validity of Eq.(10)for the transverse mass spectrum.The correlations are much more affected by deviations from the extensive statistics than the single particle observables,such as the transverse mass distribution.We can obtain a very good agreement with the experimentalresults ofΦp⊥,still being consistent with the other single particle measurements.In this context,it is worth noticing that,even for small deviations from the standard statistics,an appreciable difference in the distribution function and in thefluctuations(with respect to the standard ones)appears especiallyin the region of high transverse momenta.This behavior is consistent with the interpretation of the nonextensive statistics effects,since the detected high energy pions should be essentially the primary ones,hence more sensitive to the early stage of the collisions.In order to show this fact,we have evaluated the partial contributions to the quantityΦp⊥,by using Eq.s(14)and(15),and by extending the integration over p⊥to partial intervals∆p⊥=0.5GeV.The results are shown in Fig.2,at T=170MeV andµ=60MeV.In the standard statistics(dashed line),Φp⊥isalways positive and vanishes in the p⊥–intervals above≈1GeV.In the nonextensive statistics(solid line),instead,thefluctuation measureΦp⊥becomes negative for p⊥larger than0.5GeV and becomes vanishingly small only inp⊥–intervals above∼3GeV.In view of these considerations,we suggest an analysis of the Pb+Pb measurements which allows to disentanglethe contributions toΦp⊥in different p⊥’s intervals.A negative value ofΦp⊥at high transverse momentum intervalscould be a clear evidence of the presence of a nonextensive regime.VII.CONCLUSIONSThe nonextensive statistics appears suitable to evaluate physical observables recently measured in heavy ion collision experiments.The spectrum of the transverse momentum can be reproduced by means of the nonextensive distribution, which naturally takes into account typical collective effects in heavy colliding nuclei such as the increasing of the slopeparameter with high p⊥and high particle masses.The calculated correlation measureΦp⊥agrees with the experimentalvalue by considering a small deviation from the standard statistics.Within the nonextensive approach we have alsofound negative partial contributions toΦp⊥at high p⊥(larger than0.5GeV).In this regime theΦp⊥value is notaffected by resonance decays:hence an experimental confirmation of our prediction would be an unambiguous signalof the validity of nonextensive statistics in relativistic heavy ion collisions.The quantity q is not just a free parameter:it depends on the physical conditions generated in the reaction and,inprinciple,should be related to microscopic quantities(such as the mean interparticle interaction length,the screeninglength and the frequency collision into the parton plasma).We have found that a value of q slightly larger than one characterizes the correlation measureΦ,both by suppressing the bosonfluctuations in Eq.(15)and by enhancing theimportance of the region of large transverse momenta in Eq.(14).In the diffusional approximation,a value q>1 implies the presence of a superdiffusion among the constituent particles(the mean square displacement is not linearlyproportional to time,having,instead,a power law behavior x2 ∝tα,withα>1).Effects of anomalous diffusion are strongly related to the presence of non–Markovian memory interactions and colored noise force in the Langevin equation[41].In this context,we note that in Ref.[42],the QCD chiral phase transition is analyzed in analogy withthe metal–insulator one and it is shown that an anomalous diffusion regime can take place.The meaning of anomalousdiffusion can be found in the presence of multiparticle rescattering,which is very large in Pb+Pb collisions[6,7]. The early stage of the p+p collision is believed to be radically different from the Pb+Pb case and the influence of the nonextensive statistics appears not negligible in the last reaction.In these terms the anomalous medium effects and the remarkable experimental differences between light and heavy ion collisions should be better understood. Finally we notice that,for a given value of the deformation parameter q,the greater is the mass of the detected particle,the more strongly modified are thefluctuations.For this reason,the present calculation predicts more important nonextensive effects for the correlations of heavier mesons and baryons,than for light particles:futuremeasurements ofΦp⊥for these heavier particles should give a more clear evidence of this effect.Furthermore,thenonextensive statistics could imply a sizable modification of the hadronic mass compressibility,since this quantity is strongly related to particlefluctuations(being more sizably suppressed for particles of heavier masses1)[43].We also remind that the nonextensive statistics implies,for q>1,a suppression of the standard bosonfluctuations given in Eq.(17),which is more effective at high transverse momentum whereas it appears negligible for low momenta.Shuryak suggests[40]that enhancedfluctuations for low p⊥bins,in the pion p⊥histograms,are a possible manifestation of disoriented chiral condensation.We may argue that this effect could be much more evident if one assumes the validity of the generalized statistics.New data and investigations are necessary to gain a deeper understanding of the high energy heavy–ion observables.。
a rX iv:c ond-ma t/31521v1[c ond-m at.stat-m ec h]27J a n23Nonextensive statistical mechanics -Applications to nuclear and high energy physics ∗Constantino Tsallis Centro Brasileiro de Pesquisas F´ısicas Rua Xavier Sigaud 150,22290-180Rio de Janeiro,RJ,Brazil Ernesto P.Borges Escola Politecnica,Universidade Federal da Bahia,Rua Aristides Novis 240210-630Salvador-BA,Brazil †(February 2,2008)Abstract A variety of phenomena in nuclear and high energy physics seemingly do not satisfy the basic hypothesis for possible stationary states to be of the type covered by Boltzmann-Gibbs (BG)statistical mechanics.More specifi-cally,the system appears to relax,along time,on macroscopic states which violate the ergodic assumption.Some of these phenomena appear to follow,instead,the prescriptions of nonextensive statistical mechanics.In the same manner that the BG formalism is based on the entropy S BG =−k i p i ln p i ,the nonextensive one is based on the form S q =k (1− i p q i )/(q −1)(withS1=S BG).Typically,the systems following the rules derived from the formerexhibit an exponential relaxation with time toward a stationary state char-acterized by an exponential dependence on the energy(thermal equilibrium),whereas those following the rules derived from the latter are characterized by(asymptotic)power-laws(both the typical time dependences,and the energydistribution at the stationary state).A brief review of this theory is given here,as well as of some of its applications,such as electron-positron annihilationproducing hadronic jets,collisions involving heavy nuclei,the solar neutrinoproblem,anomalous diffusion of a quark in a quark-gluon plasma,andflux ofcosmic rays on Earth.In addition to these points,very recent developmentsgeneralizing nonextensive statistical mechanics itself are mentioned.I.INTRODUCTIONThe foundation of statistical mechanics comes from mechanics(classical,quantum,rel-ativistic,or any other elementary dynamical theory).Consistently,in our opinion,the expression of entropy to be adopted for formulating statistical mechanics(and ultimately thermodynamics)depends on the particular type of occupancy of phase space(or Hilbert space,or Fock space,or analogous space)that the microscopic dynamics of the system under study collectively favors.In other words,it appears to be nowadays strong evidence that statistical mechanics is larger than Boltzmann-Gibbs(BG)statistical mechanics,that the concept of physical entropy can be larger thanS BG=−kWip i ln p i(1)(hence S BG=k ln W for equal probabilities),pretty much as geometry is known today to be larger than Euclidean geometry,since Euclid’s celebrated parallel postulate can be properly generalized in mathematically and physically very interesting manners.Let us remind the words of A.Einstein[1]expressing his understanding of Eq.(1):Usually W is put equal to the number of complexions[...].In order to calculate W,one needs a complete(molecular-mechanical)theory of the system under consideration.Therefore it is dubious whether the Boltzmann principle has any meaning without a complete molecular-mechanical theory or some other theory which describes the elementary processes.S= R(q∈R;S1=S BG).(2)q−1It is well known that for microscopic dynamics which relax on an ergodic occupation of phase space,the adequate entropic form to be used is that of Eq.(1).Such assumption is ubiquitously satisfied,and constitutes the physical basis for the great success of BG thermostatistics since over a century.We believe that a variety of more complex occupations of phase space may be handled with more complex entropies.In particular,it seems that Eq.(2),associated with an index q which is dictated by the microscopic dynamics(and which generically differs from unity),is adequate for a vast class of stationary states ubiquitously found in Nature.In recent papers,E.G.D.Cohen[3]and M.Baranger[4]also have addressed this question.A significant amount of systems,e.g.,turbulentfluids([5,6]and references therein), electron-positron annihilation[7,8],collisions of heavy nuclei[9–11],solar neutrinos[12,13], quark-gluon plasma[14],cosmic rays[15],self-gravitating systems[17],peculiar velocities of galaxy clusters[18],cosmology[19],chemical reactions[20],economics[21–23],motion ofHydra viridissima[24],theory of anomalous kinetics[25],classical chaos[26],quantum chaos [27],quantum entanglement[28],anomalous diffusion[29],long-range-interacting many-body classical Hamiltonian systems([30]and references therein),internet dynamics[31], and others,are known nowadays which in no trivial way accommodate within BG statistical mechanical concepts.Systems like these have been handled with the functions and concepts which naturally emerge within nonextensive statistical mechanics[2,32,33].We may think of q as a biasing parameter:q<1privileges rare events,while q>1privi-leges common events.Indeed,p<1raised to a power q<1yields a value larger than p,and the relative increase p q/p=p q−1is a decreasing function of p,i.e.,values of p closer to0(rare events)are benefited.Correspondingly,for q>1,values of p closer to1(common events) are privileged.Therefore,the BG theory(i.e.,q=1)is the unbiased statistics.A concrete consequence of this is that the BG formalism yields exponential equilibrium distributions (and time behavior of typical relaxation functions),whereas nonextensive statistics yields (asymptotic)power-law distributions(and relaxation functions).Since the BG exponential is recovered as a limiting case,we are talking of a generalization,not an alternative.To obtain the probability distribution associated with the relevant stationary state(ther-mal equilibrium or metaequilibrium)of our system we must optimize the entropic form(2) under the following constraints[2,32]:p i=1,(3)iandi p q i E i,(5)Z qwhereZ q≡ j[1−(1−q)βq(E j−U q)]1/(1−q),(6) andββq≡S will be optimized by the same distribution.Nevertheless,only a very restricted class of such entropic forms can be considered as serious candidates for constructing a full thermo-statistical theory,eventually connected with thermodynamics.In particular,one expects the correct entropy to be concave and stable.Such is the case[35]of S q as well as of the generalized entropy recently proposed[36,37]for the just mentioned superstatistics[34].We briefly address these questions in this Section.Let usfirst consider the following differential equation:dy=e−t/τ.(12)O(0)−O(∞)(iii)We may refer to the energy distribution at thermal equilibrium of a Hamiltonian system,and consider x≡E i,where E i is the energy of the i-th microscopic state,y=Z p(E i),where p is the energy probability and Z the partition function,and−a≡βis the inverse temperature.In this case Eq.(10)reads in the familiar BG form:p(E i)=e−βE idx=ay q(y(0)=1).(14) The solution is given byy=e ax q≡[1+(1−q)ax]1/(1−q),(15) e x q being from now on referred to as the q-exponential function(e x1=e x).The three above possible physical interpretations of such solution now become(i)For the sensitivity to the initial conditions,ξ(t)=eλq tq=[1+(1−q)λq t]1/(1−q),(16) whereλq=0is the generalized Lyapunov coefficient(see[26]),and,at the edge of chaos,λq>0and q<1.(ii)For the relaxation,O(t)−O(∞)[1+(q−1)τq t]1/(q−1),(17) whereτq>0is a generalized relaxation time,and typically q≥1[38].(iii)For the energy distribution,we get the form which emerges in nonextensive statistical mechanics,namely[2,32]p(E i)=e−β′q E iq[1+(q−1)β′q E i]1/(q−1)(Z′q≡ j e−β′q E j q),(18)where usually,but not necessarily,β′q>0and q≥1.This distribution is the one that optimizes the entropy S q under appropriate constraints for the canonical ensemble.Let us next unify Eqs.(9)and(14)as follows:dy+1 1a1Hagedorn.This scenario is now confirmed.The ingredients for a microscopic model within this approach have also been proposed[8].Heavy nuclei collisions:A variety of high-energy collisions have been discussed in terms of the present nonexten-sive formalism.Examples include proton-proton,central Pb-Pb and other nuclear collisions [9,10].Along related lines,entropic inequalities applied to pion-nucleon experimental phase shifts have provided strong evidence of nonextensive quantum statistics[11].Solar neutrino problem:The solar plasma is believed to produce large amounts of neutrinos through a variety of mechanisms(e.g.,the proton-proton chain).The calculation done using the so called Solar Standard Model(SSM)results in a neutrinoflux over the Earth,which is roughly the double of what is measured.This is sometimes referred to as the neutrino problem or the neutrino enigma.There is by no means proof that this neutrinoflux defect is due toa single cause.It has recently been verified that neutrino oscillations do seem to exist([12]and references therein),which would account for part of the deficit.But it is not at all clear that it would account for the entire discrepancy.Quarati and collaborators[13] argue that part of it–even,perhaps,an appreciable part of it–could be due to the fact that BG statistical mechanics is used within the SSM.The solar plasma involves turbulence, long-range interactions,possibly long-range memory processes,all of them phenomena that could easily defy the applicability of the BG formalism.Then they show[13]in great detail how the modification of the“tail”of the energy distribution could considerably modify the neutrinoflux to be expected.Consequently,small departures from q=1(e.g.,|q−1|of the order of0.1)would be enough to produce as much as50%difference in theflux.This is due to the fact that most of the neutrinoflux occurs at what is called the Gamow peak. This peak occurs at energies quite above the temperature,i.e.,at energies in the tail of the distribution.Quark diffusion:The anomalous diffusion of a charm quark in a quark-gluon plasma has been analyzed byWalton and Rafelski[14]through both nonextensive statistical mechanical arguments and quantum chromodynamics.The results coincide,as they should,only for q=1.114. Cosmic rays:ThefluxΦof cosmic rays arriving on Earth is a quantity whose measured range is among the widest experimentally known(33decades in fact).This distribution refers to a range of energies E which also is impressive(13decades).This distribution is very far from exponential:See Figs.1and2.This basically indicates that no BG thermal equilibrium is achieved,but some other(either stationary,or relatively slow varying)state,characterized in fact by a power law.If the distribution is analyzed with more detail,one verifies that two,and not one,power-law regimes are involved,separated by what is called the“knee”(slightly below1016eV).At very high energies,the power-law seems to be interrupted by what is called the“ankle”(close to1019eV)and perhaps a cutoff.The momentaM l≡ (E− E )l =[ E cutof f0dEΦ(E)(E− E )l]/[ E cutof fdEΦ(E)](l=1,2,3)as functionsof the cutoffenergy E cutoff(assumed to be abrupt for simplicity)are calculated as well:See Figs.3,4and5.At high cutoffenergies, E saturates at2.48944...×109eV[15],a value which is over ten times larger than the Hagedorn temperature(close to1.8×108eV[8]).In the same limit,we obtain for the specific-heat-like quantity M2≃ E2 ≃6.29×1021(eV)2. Finally,M3≃ E3 diverges with increasing E cutoff.This is of course due to the fact that, in the high energy limit,Φ∝1/E1dE i=−b′p q′i−bp q i.(21)This differential equation has remarkable particular cases.The most famous one is(q′,q)= (1,2),since it precisely corresponds to the differential equation which enabled Planck,in his October1900paper,to(essentially)guess the black-body radiation distribution,thus opening(together with his December1900paper)the road to quantum mechanics.The more general case q′=1and arbitrary q is a simple particular instance of the Bernoulli equation,and,as such,has a simple explicit solution(Eq.(20)with a1=−b′and a q=−b). This solution has proved its efficiency in a variety of problems,including in generalizing the Zipf-Mandelbrot law for quantitative linguistics(for a review,see Montemurro’s article in the Gell-Mann–Tsallis volume[33]).Finally,the generic case q>q′>1also has an explicit solution(though not particularly simple,but in terms of two hypergeometric functions; see[38])and produces,taking also into account the ultra-relativistic ideal gas density of states,the above mentioned quite good agreement with the observedfluxes.Indeed,if we assume0<b′<<b and q′<q,the distribution makes a neat crossover from a power-law characterized by q at low energies to a power-law characterized by q′at high energies, which is exactly what the cosmic rays exhibit to a quite good approximation.Let usfinally mention that thefirst possible microscopic interpretation of our phenomenological theory has just been suggested[39].For possible effects of a slightly nonextensive black-body radiation on cosmic rays see [40].Finally,other aspects related to cosmic rays have been shown to exhibitfingerprints of nonextensivity[41].IV.CONCLUSIONSIn nuclear and high energy physics,there is a considerable amount of anomalous phe-nomena that benefit from a thermostatistical treatment which exceeds the usual capabilities of Boltzmann-Gibbs statistical mechanics.This fact is due to the relevance of long-range forces,as well as to a variety of dynamical nonlinear dynamical aspects,possibly leading to nonmarkovian processes,i.e.,long-term microscopic memory.Some of these phenomenaappear to be tractable within nonextensive statistical mechanics,and we have illustrated this with a few typical examples.For the particular case of cosmic rays,we have indi-cated their average energy E ≃2.48944...×109eV,and the specific-heat-like quantity E2 − E 2≃6.29×1021(eV)2,with the hope that they might be usefully compared to related astrophysical quantities,either already available in the literature,or to be studied. Along the same vein we have also presented the dependence of such momenta on a possibly existing high-energy cutoff.In addition to this,we have sketched the possible generalization of nonextensive statistical mechanics on the basis of a recently introduced entropic form[36],whose stationary state is the Beck-Cohen superstatistics[34].The metaequilibrium distribution associated with a crossover between q-statistics and q′-statistics can be seen as a particular case of this generalized nonextensive statistical mechanics.It is worthy to mention at this point that the present attempts for further generalization of BG statistical mechanics are to be understood on physical grounds,and by no means as informational quantities that can be freely introduced to deal with specific tasks,and which can in principle depend on as many free(orfitting)parameters as one wishes.Examples of such informational quantities are the Renyi entropy(depending on one parameter and being usefully applied in the multifractal characterization of chaos),Sharma-Mittal entropy (which contains both Renyi entropy and S q as particular cases),and very many others that are available in the literature.The precise criteria for an entropic form to be considered a possible physical entropy are yet not fully understood,although it is already clear that it must have a microscopic dynamical foundation.It seems however reasonable to exclude,at this stage,those forms which,in contrast with S BG and S q,(i)are not concave(or convex),since this would seriously damage the capability for thermodynamical stability and for satisfactory thermalization of different systems put in thermodynamical contact,or(ii)are not stable, since this would imply that the associated quantity would not be robust under experimental measurements.These crucial points,and several others(probably equally important,such as thefinite entropy production per unit time),have been disregarded by Luzzi et al[42]in theirrecent criticism of nonextensive statistical mechanics.Indeed,Renyi entropy,Sharma-Mittal entropy(that Luzzi et al mention without any justification at the same epistemological level as S q)are neither concave nor stable for arbitrary values of their parameters.These and other information measures(most of them not concave and/or not stable)have been freely introduced,along various decades,as optimizing tools for specific tasks.They can certainly be useful for various purposes,which do not necessarily include the specific one we are addressing here:a thermodynamically meaningful generalization of the Boltzmann-Gibbs physical entropy.ACKNOWLEDGMENTSWe are indebted to T.Kodama,G.Wilk,I.Bediaga,E.G.D.Cohen,M.Baranger and J. 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Distributions,Nonlinear Dynamics,and Nonextensiv-ity,Physica D(2003),in preparation.An updated bibliography can be found at the web site http://tsallis.cat.cbpf.br/biblio.htm[34]C.Beck and E.G.D.Cohen,Superstatistics,Physica A(2003),in press[cond-mat/0205097].[35]S.Abe,Phys.Rev.E66,046134(2002).[36]C.Tsallis and A.M.C.Souza,Constructing a statistical mechanics for Beck-Cohen su-perstatistics,Phys.Rev.E67,0261XX(1Feb2003),in press[cond-mat/0206044]. 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