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An Introduction to Statistical Mechanics and Thermodynamics最新文献

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Discrete Probability Theory 离散概率论
An Introduction to Statistical Mechanics and Thermodynamics Pub Date : 2012-03-01 DOI: 10.1093/acprof:oso/9780199646944.003.0003
R. Swendsen
{"title":"Discrete Probability Theory","authors":"R. Swendsen","doi":"10.1093/acprof:oso/9780199646944.003.0003","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646944.003.0003","url":null,"abstract":"The chapter presents an overview of various interpretations of probability. It introduces a ‘model probability,’ which assumes that all microscopic states that are essentially alike have the same probability in equilibrium. A justification for this fundamental assumption is provided. The basic definitions used in discrete probability theory are introduced, along with examples of their application. One such example, which illustrates how a random variable is derived from other random variables, demonstrates the use of the Kronecker delta function. The chapter further derives the binomial and multinomial distributions, which will be important in the following chapter on the configurational entropy, along with the useful approximation developed by Stirling and its variations. The Gaussian distribution is presented in detail, as it will be very important throughout the book.","PeriodicalId":102491,"journal":{"name":"An Introduction to Statistical Mechanics and Thermodynamics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126747655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Consequences of Extensivity 广泛性的后果
An Introduction to Statistical Mechanics and Thermodynamics Pub Date : 2012-03-01 DOI: 10.1093/ACPROF:OSO/9780199646944.003.0013
R. Swendsen
{"title":"The Consequences of Extensivity","authors":"R. Swendsen","doi":"10.1093/ACPROF:OSO/9780199646944.003.0013","DOIUrl":"https://doi.org/10.1093/ACPROF:OSO/9780199646944.003.0013","url":null,"abstract":"While not all thermodynamic systems are extensive, those that are homogeneous satisfy the useful postulate of extensivity. In this chapter we return to the thermodynamic postulates and consider the consequences of extensivity. The Euler equation can be derived from extensivity, and the Gibbs–Duhem equation can be derived from the Euler equation. The Gibbs–Duhem equation shows that changes in the chemical potential are not arbitrary, but are determined by changes in the temperature and pressure for. That in turn simplifies the reconstruction of the fundamental equation from the equations of state. The Euler equation also allows the various thermodynamic potentials to be rewritten in terms of other functions.","PeriodicalId":102491,"journal":{"name":"An Introduction to Statistical Mechanics and Thermodynamics","volume":"60 23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125129658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ideal Quantum Gases 理想量子气体
An Introduction to Statistical Mechanics and Thermodynamics Pub Date : 2012-03-01 DOI: 10.1093/acprof:oso/9780199646944.003.0026
R. Swendsen
{"title":"Ideal Quantum Gases","authors":"R. Swendsen","doi":"10.1093/acprof:oso/9780199646944.003.0026","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646944.003.0026","url":null,"abstract":"As a preliminary to discussing the properties of Bose–Einstein and Fermi–Dirac gases, this chapter presents the basic quantum equations that underlie both. The process of building N-body states from single-particle states is described, along with notation necessary to simplify the problem. The average number of particles in a given energy state and chemical potential is derived for fermions and bosons. Although all atoms are either bosons or fermions, and therefore indistinguishable, there are nevertheless real systems that are composed of distinguishable particles. Although all atoms are either bosons or fermions, and therefore indistinguishable, there are nevertheless real systems that are composed of distinguishable particles.","PeriodicalId":102491,"journal":{"name":"An Introduction to Statistical Mechanics and Thermodynamics","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122356979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Insulators and Semiconductors 绝缘体和半导体
An Introduction to Statistical Mechanics and Thermodynamics Pub Date : 2012-03-01 DOI: 10.1093/acprof:oso/9780199646944.003.0029
R. Swendsen
{"title":"Insulators and Semiconductors","authors":"R. Swendsen","doi":"10.1093/acprof:oso/9780199646944.003.0029","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646944.003.0029","url":null,"abstract":"The origin of the strange band gaps that arise in the electron density of states in real materials is that the regular arrangement of the nuclei in a crystal lattice creates a periodic potential. This affects the energy levels of the electrons and gives rise to gaps in the energy spectrum. The properties of insulators and semiconductors are very important in modern technology. They are largely due to the Fermi–Dirac statistics obeyed by electrons. Following the discussion of the behavior of free electrons in the previous chapter, this one turns to the properties that emerge when electrons are subject to a periodic potential, as they are in a crystal. The periodic potential leads to Bloch's theorem, band theory, and the prediction of band gaps, which are responsible for the differences in the properties of metals, insulators, and semiconductors. Dopants and their basic effects are discussed.","PeriodicalId":102491,"journal":{"name":"An Introduction to Statistical Mechanics and Thermodynamics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124333632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
The Nernst Postulate: The Third Law of Thermodynamics 能量假设:热力学第三定律
An Introduction to Statistical Mechanics and Thermodynamics Pub Date : 2012-03-01 DOI: 10.1093/ACPROF:OSO/9780199646944.003.0018
R. Swendsen
{"title":"The Nernst Postulate: The Third Law of Thermodynamics","authors":"R. Swendsen","doi":"10.1093/ACPROF:OSO/9780199646944.003.0018","DOIUrl":"https://doi.org/10.1093/ACPROF:OSO/9780199646944.003.0018","url":null,"abstract":"The Nernst postulate, or Third Law of Thermodynamics, is derived from quantum statistical mechanics. It states, ‘The entropy of a thermodynamic system goes to a constant as the temperature goes to zero.’ The main consequences are that specific heat and compressibility goes to zero as temperature goes to zero. Both are demonstrated. It is shown that, both with and without the Nernst postulate, zero temperature is not experimentally attainable. Gases are usually well behaved in this respect, but we all know from experience that molecules of H2O can clump together, form drops, and rain on us.","PeriodicalId":102491,"journal":{"name":"An Introduction to Statistical Mechanics and Thermodynamics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131071033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum Canonical Ensemble 量子正则系综
An Introduction to Statistical Mechanics and Thermodynamics Pub Date : 2012-03-01 DOI: 10.1093/ACPROF:OSO/9780199646944.003.0023
R. Swendsen
{"title":"Quantum Canonical Ensemble","authors":"R. Swendsen","doi":"10.1093/ACPROF:OSO/9780199646944.003.0023","DOIUrl":"https://doi.org/10.1093/ACPROF:OSO/9780199646944.003.0023","url":null,"abstract":"This chapter introduces the quantum mechanical canonical ensemble, which is used for the majority of problems in quantum statistical mechanics. The ensemble is derived and analogies with the classical ensemble are presented. A useful expression for the quantum entropy is derived. The origin of the Third Law is explained. The relationship between fluctuations and derivatives found in classical statistical mechanics is shown to have counterparts in quantum statistical mechanics. The factorization of the partition function is re-introduced as the best trick in quantum statistical mechanics. Due to their importance in later chapters, basic calculations of the properties of two-level systems and simple harmonic oscillators are derived.","PeriodicalId":102491,"journal":{"name":"An Introduction to Statistical Mechanics and Thermodynamics","volume":"10862 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123463504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Phase Transitions and the Ising Model 相变和伊辛模型
An Introduction to Statistical Mechanics and Thermodynamics Pub Date : 2012-03-01 DOI: 10.1093/ACPROF:OSO/9780199646944.003.0030
R. Swendsen
{"title":"Phase Transitions and the Ising Model","authors":"R. Swendsen","doi":"10.1093/ACPROF:OSO/9780199646944.003.0030","DOIUrl":"https://doi.org/10.1093/ACPROF:OSO/9780199646944.003.0030","url":null,"abstract":"Chapter 17 presented one example of a phase transition, the van der Waals gas. This chapter provides another, the Ising model, a widely studied model of phase transitions. We first give the solution for the Ising chain (one-dimensional model), including the introduction of the transfer matrix method. Higher dimensions are treated in the Mean Field Approximation (MFA), which is also extended to Landau theory. The Ising model is deceptively simple. It can be defined in a few words, but it displays astonishingly rich behavior. It originated as a model of ferromagnetism in which the magnetic moments were localized on lattice sites and had only two allowed values.","PeriodicalId":102491,"journal":{"name":"An Introduction to Statistical Mechanics and Thermodynamics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116785633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Perturbations of Thermodynamic State Functions 热力学态函数的微扰
An Introduction to Statistical Mechanics and Thermodynamics Pub Date : 2012-03-01 DOI: 10.1093/acprof:oso/9780199646944.003.0010
R. Swendsen
{"title":"Perturbations of Thermodynamic State Functions","authors":"R. Swendsen","doi":"10.1093/acprof:oso/9780199646944.003.0010","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646944.003.0010","url":null,"abstract":"Because small changes in thermodynamic quantities will play a central role in much of the development of thermodynamics, the key concepts are introduced in this short chapter. The First Law (conservation of energy) can be expressed simply in terms of infinitesimal quantities: a small change in the energy of a system is equal to the heat added plus the work done on the system. The theories of statistical mechanics and thermodynamics deal with the same physical phenomena. Exact and inexact differentials are defined, along with the important concept of an integrating factor that relates them. The useful equation relating small changes in heat to corresponding changes in entropy is derived.","PeriodicalId":102491,"journal":{"name":"An Introduction to Statistical Mechanics and Thermodynamics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116746489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Postulates and Laws of Thermodynamics 热力学假设和定律
An Introduction to Statistical Mechanics and Thermodynamics Pub Date : 2012-03-01 DOI: 10.1093/acprof:oso/9780199646944.003.0009
R. Swendsen
{"title":"The Postulates and Laws of Thermodynamics","authors":"R. Swendsen","doi":"10.1093/acprof:oso/9780199646944.003.0009","DOIUrl":"https://doi.org/10.1093/acprof:oso/9780199646944.003.0009","url":null,"abstract":"The points of view about the behavior of macroscopic systems arising from thermodynamics and statistical mechanics are compared and contrasted. The concept of a state function is explained, and the postulates of thermodynamics, which describe fundamental properties of the entropy, are presented. Some are essential postulates, which are always valid, while others, called optional postulates, are very useful when they do apply. The Laws of Thermodynamics are derived from these postulates. With this chapter we begin the formal study of thermodynamics, which represents a detour from the development of the foundations of classical statistical mechanics that we began in Part I.","PeriodicalId":102491,"journal":{"name":"An Introduction to Statistical Mechanics and Thermodynamics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127431225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classical Ensembles: Grand and Otherwise 古典合奏:大的和其他的
An Introduction to Statistical Mechanics and Thermodynamics Pub Date : 2012-03-01 DOI: 10.1093/ACPROF:OSO/9780199646944.003.0020
R. Swendsen
{"title":"Classical Ensembles: Grand and Otherwise","authors":"R. Swendsen","doi":"10.1093/ACPROF:OSO/9780199646944.003.0020","DOIUrl":"https://doi.org/10.1093/ACPROF:OSO/9780199646944.003.0020","url":null,"abstract":"The chapter introduces the grand canonical ensemble as a means of describing systems that exchange particles with a reservoir. The grand canonical partition function is defined in general and calculated for the ideal gas in particular. Other ensembles are described and their relationship to the grand canonical ensemble is shown. The physical situation described by the grand canonical ensemble is that of a system that can exchange both energy and particles with a reservoir. As usual, we assume that the reservoir is much larger than the system of interest, so that its properties are not signifficantly affected by relatively small changes in its energy or particle number.","PeriodicalId":102491,"journal":{"name":"An Introduction to Statistical Mechanics and Thermodynamics","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127346906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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