圖書信息
出版社: 世界圖書出版公司; 第1版 (2011年6月1日)
外文書名: Entropy,Large Deviations,and Statistical Mechanics
平裝: 364頁
正文語種: 英語
開本: 24
ISBN: 9787510035111
條形碼: 9787510035111
尺寸: 22 x 14.8 x 1.8 cm
重量: 481 g
作者簡介
作者：(美國)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.
內容簡介
《熵大偏差和統計力學(英文)》主要內容簡介：This book has two main topics: large deviations and equilibrium statistical mechanics. I hope to convince the reader that these topics have many points of contact and that in being treated together, they enrich each other. Entropy,in its various guises, is their common core.
目錄
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
