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  • 熵大偏差和统计力学(英文)[平装]
  • 共2个商家     39.20元~44.59
  • 作者:艾里斯(RichardS.Ellis)(作者)
  • 出版社:世界图书出版公司;第1版(2011年6月1日)
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  • ISBN:9787510035111

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    《熵大偏差和统计力学(英文)》由世界图书出版公司出版。

    作者简介

    作者:(美国)艾里斯 (Richard S.Ellis)

    艾里斯,Richard S.Ellis,received his B.A. degree in mathematics and German literature from Harvard University in 1969 and his Ph.D. degree in mathematics from New York University in 1972. After spending three years at Northwestern University, he moved to the University of Massachusetts, Amherst, where he is a Professor in the Department of Mathematics and Statistics and Adjunct Professor in the Depart-ment of Judaic and Near Eastern Studies. His research interests in mathematics focus on the theory of large deviations and on applica-tions to statistical mechanics and other areas.

    目录

    Preface
    Comments on the Use of This Book
    PART 1: LARGE DEVIATIONS AND STATISTICAL MECHANICS
    Chapter 1. Introduction to Large Deviations
    Overview
    Large Deviations for 1.I.D. Random Variables with a Finite State
    Space
    Levels-1 and 2 for Coin Tossing
    Levels-1 and 2 for I.I.D. Random Variables with a Finite State
    Space
    Level-3: Empirical Pair Measure
    Level-3: Empirical Process
    Notes
    Problems
    Chapter 2. Large Deviation Property and Asymptotics of Integrals
    Introduction
    Levels-l, 2, and 3 Large Deviations for I.I.D. Random Vectors
    The Definition of Large Deviation Property
    Statement of Large Deviation Properties for Levels-l, 2, and 3
    Contraction Principles
    Large Deviation Property for Random Vectors and Exponential
    Convergence
    Varadhan's Theorem on the Asymptotics of Integrals
    Notes
    Problems
    Chapter 3. Large Deviations and the Discrete Ideal Gas
    Introduction
    Physics Prelude: Thermodynamics
    The Discrete Ideal Gas and the Microcanonical Ensemble
    Thermodynamic Limit, Exponential Convergence, and
    Equilibrium Values
    The Maxwell-Boltzmann Distribution and Temperature
    The Canonical Ensemble and Its Equivalence with the
    Microcanonical Ensemble
    A Derivation of a Thermodynamic Equation
    The Gibbs Variational Formula and Principle
    Notes
    Problems
    Chapter 4. Ferromagnetic Models on Z
    Introduction
    An Overview of Ferromagnetic Models
    Finite-Volume Gibbs States on Z
    Spontaneous Magnetization for the Curie-Weiss Model
    Spontaneous Magnetization for General Ferromagnets on Z
    Infinite-Volume Gibbs States and Phase Transitions
    The Gibbs Variational Formula and Principle
    Notes
    Problems
    Chapter 5. Magnetic Models on Zn and on the Circle
    Introduction
    Finite-Volume Gibbs States on ZD, D > 1
    Moment Inequalities
    Properties of the Magnetization and the Gibbs Free Energy
    Spontaneous Magnetization on ZD, D >2, Via the Peierls Argument
    Infinite-Volume Gibbs States and Phase Transitions
    Infinite-Volume Gibbs States and the Central Limit Theorem
    Critical Phenomena and the Breakdown of the Central Limit
    Theorem
    Three Faces of the Curie-Weiss Model
    The Circle Model and Random Waves
    A Postscript on Magnetic Models
    Notes
    Problems

    PART 2: CONVEXITY AND PROOFS OF LARGE DEVIATION
    THEOREMS
    Chapter 6. Convex Functions and the Legendre-Fenchel Transform
    Introduction
    Basic Definitions
    Properties of Convex Functions
    ……
    APPENDICES

    文摘

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    In the next three chapters we apply the theory of large deviations to analyze some basic models in equilibrium statistical mechanics.' This branch of physics applies probability theory to study equilibrium properties of systems consisting of a large number of particles. The systems fall into two groups:continuous systems, which include the solids, liquids, and gases common to everyday experience; and lattice systems, of which ferromagnets are the main example. This chapter introduces the continuous theory by treating a simple model called a discrete ideal gas. This model, which has no interactions, is a physical analog of i.i.d, random variables.
    The macroscopic description of a physical system such as an ideal gas isgiven by thermodynamics. Thermodynamics summarizes the properties ofthe gas in terms of macroscopic variables such as pressure, volume, tempera- ture, and internal energy. But this theory takes no account of the fact that the gas is composed ofrnolecules. The main aim of statistical mechanics is to derive properties of the gas from a probability distribution which describes its microscopic (i.e., molecular) behavior. This distribution is called an ensemble.