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书名 熵大偏差和统计力学
分类 科学技术-自然科学-数学
作者 (美)艾里斯
出版社 世界图书出版公司
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《熵大偏差和统计力学》是一部教程,内容上相对独立,自成体系。书中大偏差的讲述除了为这科目做出了巨大贡献,也将统计力学的好多方面完美结合,并且很具有数学吸引力。而且作者在没有假设读者具有丰富的物理知识背景下讲述,使得本书能够让更多的读者学习理解。每章末都附有一节注解和一节问题,这100来道练习题,附有许多提示,使得本书更加易于学习理解。本书由艾里斯编。

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

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