统计力学 : 非平衡态热力学的随机方法 : 第2版

Preface

Classical Statistical Dynamics

1.Introduction

2.Probability Theory

2.1 Sample Spaces and States

2.2 Random Variables, Algebras

2.3 Entropy

2.4 Exercises

3.Linear Dynamics

3.1 Reversible Dynamics

3.2 Random Dynamics

3.3 Convergence to Equilibrium

3.4 Markov Chains

3.5 Exercises

4.Isolated Dynamics

Preface

Classical Statistical Dynamics

1.Introduction

2.Probability Theory

2.1  Sample Spaces and States

2.2  Random Variables, Algebras

2.3  Entropy

2.4  Exercises

3.Linear Dynamics

3.1  Reversible Dynamics

3.2  Random Dynamics

3.3  Convergence to Equilibrium

3.4  Markov Chains

3.5  Exercises

4.Isolated Dynamics

4.1  The Boltzmann Map

4.2  The Heat-Particle

4.3  The Hard-Core Model of Chemical Kinetics

4.3.1  Isomers and Diffusion in a Force-Field

4.3.2  Markov Dynamics

4.3.3  Entropy Production

4.3.4  Osmosis

4.3.5  Exchange Diffusion

4.3.6  General Diffusions

4.4  Chemical Reactions

4.4.1  Unimolecular Reactions

4.4.2  Balanced Reactions

4.5  Energy of Solvation

4.6  Activity-led Reactions

4.7  Exercises

5.Isothermal Dynamics

5.1  Legendre Transforms

5.2  The Free-energy Theorem

5.3  Chemical Kinetics

5.4  Convergence in Norm

5.5  Dilation of Markov Chains

5.6  Exercises

6.Driven Systems

6.1  Sources and Sinks

6.2  A Poor Conductor

6.3  A Driven Chemical System

6.4  How to Add Noise

6.5  Exercises

7.Fluid Dynamics

7.1  Hydrostatics of a Gas of Hard Spheres

7.2  The Fundamental Equation

7.3  The Euler Equations

7.4  Entropy Production

7.5  A Correct Navier-Stokes System

Quantum Statistical Dynamics

8.Introduction to Quantum Theory

9.Quantum Probability

9.1  Algebras of Observables

9.2  States

9.3  Quantum Entropy

9.4  Exercises

10.Linear Quantum Dynamics

10.1  Reversible Dynamics

10.2  Random Quantum Dynamics

10.3  Quantum Dynamical Maps

10.4  Exercises

11.Isolated Quantum Dynamics

11.1  The Quantum Boltzmann Map

11.2  The Quantum Heat-Particle

11.3  Fermions and Ions with a Hard Core

11.4  The Quantum Boltzmann Equation

11.5  Exercises

12.Isothermal and Driven Systems

12.1  Isothermal Quantum Dynamics

12.2  Convergence to Equilibrium

12.3  Driven Quantum Systems

12.4  Exercises

13.Infinite Systems

13.1  The Algebra of an Infinite System

13.2  The Reversible Dynamics

13.3  Return to Equilibrium

13.4  Irreversible Linear Dynamics

13.5  Exercises

14.Proof of the Second Law

14.1  yon Neumann Entropy

14.2  Entropy Increase in Quantum Mechanics

14.3  The Quantum Kac Model

14.4  Equilibrium

14.5  The e-Limit

14.6  The Marginals and Entropy

14.7  The Results

15.Information Geometry

15.1  The Jaynes-Ingarden Theory

15.2  Non-Linear Ising Dynamics

15.3  Ising Model Close to Equilibrium

15.4  Non-linear Heisenberg Model

15.5  Estimation; the Cramer-Rao Inequality

15.6  Efron, Dawid and Amari

15.7  Entropy Methods, Exponential Families

15.8  The Work of Pistone and Sempi

15.9  The Finite-Dimensional Quantum Info-Manifold

15.10  Araki's Expansionals and the Analytic Manifold

15.11  The Quantum Young Function

15.12  The Quantum Cramer Class

15.13  The Parameter-Free Quantum Manifold

15.14  Exercises

Bibliography

Index

《统计力学——非平衡态热力学的随机方法（第二版）(英文影印版)》详细地介绍了用统计力学方法处理非平衡态热力学和统计物理问题的研究。其中统计方法包含了经典统计和量子统计。本书研究对象主要为平均能量守恒和熵增的系统。探讨了热噪声、化学反应、扩散等等问题。
　　《统计力学——非平衡态热力学的随机方法（第二版）(英文影印版)》可作为统计物理、凝聚态物理、材料科学领域的研究者的参考书，也可供相关领域研究生作为教材使用。

统计力学无疑是现代物理学的基石之一。考虑到多粒子体系，统计力学是不能绕过的、必备的工具。另外，几乎所有日常的物理学应用都与统计力学有关。《统计力学——非平衡态热力学的随机方法（第二版）(英文影印版)》作为统计力学的专著，侧重于非平衡态热力学问题，是由至于这一方面研究的学者和研究生不应错过的佳作。