伦敦地区的几所大学，在硕士研究生的最后一年，都要联合起来，通过网络教育的方式，给硕士生讲授几门统一的高级课程，本书就是其中的教程之一。本门教程在成书之前，作者已经系统地讲授了十多年，成书过程中又组织学生、同行和由出版社委派的专家一道，对书稿提出许多建议，然后再修改而成现在这个样子。

全书用一种统一的观点处理热力学和统计物理论题。第一、第二章分别讲述统计力学的方法论和理想体系的实际计算。其中差不多有一半内容属于本科期间已有的基础知识，但采用更高的、完全用统一的观点，看待热力学和统计力学。第三章非理想气体，重点讲述维里展开、配分函数、节流和状态方程。第四章相变，介绍相图、对称性、序参量、临界指数、标度理论、一级相变、二级相变、伊辛模型、朗道理论、铁电体、二元混合物、量子相变、平均场理论等等。这是全书的重点。第五章讲述涨落和动力学行为，重点是涨落的关联特性、布朗运动、朗之万方程和线性响应理论。

全书用一种统一的观点处理热力学和统计物理论题。第一、第二章分别讲述统计力学的方法论和理想体系的实际计算。其中差不多有一半内容属于本科期间已有的基础知识，但采用更高的、完全用统一的观点，看待热力学和统计力学。第三章非理想气体，重点讲述维里展开、配分函数、节流和状态方程。第四章相变，介绍相图、对称性、序参量、临界指数、标度理论、一级相变、二级相变、伊辛模型、朗道理论、铁电体、二元混合物、量子相变、平均场理论等等。这是全书的重点。第五章讲述涨落和动力学行为，重点是涨落的关联特性、布朗运动、朗之万方程和线性响应理论。

Preface

1 The Methodology of Statistical Mechanics

　1.1 Terminology and Methodology

　　1.1.1 Approaches to the subject

　　1.1.2 Description of states

　　1.1.3 Extensivity and the thermodynamic limit

　1.2 The Fundamental Principles

　　1.2.1 The laws of thermodynamics

　　1.2.2 Probabilistic interpretation of the First Law

　　1.2.3 Microscopic basis for entropy

　1.3 Interactions —The Conditions for Equilibrium

　　1.3.1 Thermal interaction—Temperature

　　1.3.2 Volume change—Pressure

　　1.3.3 Particle interchange—Chemical potential

　　1.3.4 Thermal interaction with the rest of the world—The Boltzmann factor

　　1.3.5 Particle and energy exchange with the rest of the world —The Gibbs factor

　1.4 Thermodynamic Averages

　　1.4.1 The partition function

　　1.4.2 Generalised expression for entropy

　　1.4.3 Free energy

　　1.4.4 Thermodynamic variables

　　1.4.5 Fluctuations

　　1.4.6 The grand partition function

　　1.4.7 The grand potential

　　1.4.8 Thermodynamic variables

　1.5 Quantum Distributions

　　1.5.1 Bosons and fermions

　　1.5.2 Grand potential for identical particles

　　1.5.3 The Fermi distribution

　　1.5.4 The Bose distribution

　　1.5.5 The classical limit—The Maxwell distributior

　1.6 Classical Statistical Mechanics

　　1.6.1 Phase space and classical states

　　1.6.2 Boltzmann and Gibbs phase spaces

　　1.6.3 The Fundamental Postulate in the classical case

　　1.6.4 The classical partition function

　　1.6.5 The equipartition theorem

　　1.6.6 Consequences of equipartition

　　1.6.7 Liouville's theorem

　　1.6.8 Boltzmann's H theorem

　1.7 The Third Law of Thermodynamics

　　1.7.1 History of the Third Law

　　1.7.2 Entropy

　　1.7.3 Quantum viewpoint

　　1.7.4 Unattainability of absolute zero

　　1.7.5 Heat capacity at low temperatures

　　1.7.6 Other consequences of the Third Law

　　1.7.7 Pessimist's statement of the laws of thermodynamics

2 Practical Calculations with Ideal Systems

　2.1 The Density of States

　　2.1.1 Non-interacting systems

　　2.1.2 Converting sums to integrals

　　2.1.3 Enumeration of states

　　2.1.4 Counting states

　　2.1.5 General expression for the density of states

　　2.1.6 General relation between pressure and energy

　2.2 Identical Particles

　　2.2.1 Indistinguishability

　　2.2.2 Classical approximation

　2.3 Ideal Classical Gas

　　2.3.1 Quantum approach

　　2.3.2 Classical approach

　　2.3.3 Thermodynamic properties

　　2.3.4 The l/N! term in the partition function

　　2.3.5 Entropy of mixing

　2.4 Ideal Fermi Gas

　　2.4.0 Methodology for quantum gases

　　2.4.1 Fermi gas at zero temperature

　　2.4.2 Fermi gas at low temperatures—simple model

　　2.4.3 Fermi gas at low temperatures—series expansion

　　　Chemical potential

　　　Internal energy

　　　Thermal capacity

　　2.4.4 More general treatment of low temperature heat capacity

　　2.4.5 High temperature behaviour—the classical limit

　2.5 Ideal Bose Gas

　　2.5.1 General procedure for treating the Bose gas

　　2.5.2 Number of particles—chemical potential

　　2.5.3 Low temperature behaviour of Bose gas

　　2.5.4 Thermal capacity of Bose gas—below Tc

　　2.5.5 Comparison with superfluid4 He and other systems

　　2.5.6 Two-fluid model of superfluid 4He

　　2.5.7 Elementary excitations

　2.6 Black Body Radiation—The Photon Gas

　　2.6.1 Photons as quantised electromagnetic waves

　　2.6.2 Photons in thermal equilibrium—black body radiation

　　2.6.3 Planck's formula

　　2.6.4 Internal energy and heat capacity

　　2.6.5 Black body radiation in one dimension

　2.7 Ideal Paramagnet

　　2.7.1 Partition function and free energy

　　2.7.2 Thermodynamic properties

　　2.7.3 Negative temperatures

　　2.7.4 Thermodynamics of negative temperatures

3 Non-Ideal Gases

　3.1 Statistical Mechanics

　　3.1.1 The partition function

　　3.1.2 Cluster expansion

　　3.1.3 Low density approximation

　　3.1.4 Equation of state　　

　3.2 The Virial Expansion

　　3.2.1 Virial coefficients

　　3.2.2 Hard core potential

　　3.2.3 Square-well potential

　　3.2.4 Lennard-Jones potential

　　3.2.5 Second virial coefficient for Bose and Fermi gas

　3.3 Thermodynamics

　　3.3.1 Throttling

　　3.3.2 Joule-Thomson coefficient

　　3.3.3 Connection with the second virial coefficient..

　　3.3.4 Inversion temperature

　3.4 Van der Waals Equation of State

　　3.4.1 Approximating the partition function

　　3.4.2 Van der Waals equation

　　3.4.3 Microscopic "derivation" of parameters

　　3.4.4 Virial expansion

　3.5 Other Phenomenological Equations of State

　　3.5.1 The Dieterici equation

　　3.5.2 Virial expansion

　　3.5.3 The Berthelot equation

4 Phase Transitions

　4.1 Phenomenology

　　4.1.1 Basic ideas

　　4.1.2 Phase diagrams

　　4.1.3 Symmetry

　　4.1.4 Order of phase transitions

　　4.1.5 The order parameter

　　4.1.6 Conserved and non-conserved order parameters

　　4.1.7 Critical exponents

　　4.1.8 Scaling theory

　　4.1.9 Scaling of the free energy

　4.2 First-Order Transition—An Example

　　4.2.1 Coexistence

　　4.2.2 Van der Waals fluid

　　4.2.3 The Maxwell construction

　　4.2.4 The critical point

　　4.2.5 Corresponding states

　　4.2.6 Dieterici's equation

　　4.2.7 Quantum mechanical effects

　4.3 Second-Order Transition—An Example

　　4.3.1 The ferromagnet

　　4.3.2 The Weiss model

　　4.3.3 Spontaneous magnetisation

　　4.3.4 Critical behaviour

　　4.3.5 Magnetic susceptibility

　　4.3.6 Goldstone modes

　4.4 The Ising and Other Models

　　4.4.1 Ubiquity of the Ising model

　　4.4.2 Magnetic case of the Ising model

　　4.4.3 Ising model in one dimension

　　4.4.4 Ising model in two dimensions

　　4.4.5 Mean field critical exponents

　　4.4.6 The XY model

　　4.4.7 The spherical model

　4.5 Landau Treatment of Phase Transitions

　　4.5.1 Landau free energy

　　4.5.2 Landau free energy for the ferromagnet

　　4.5.3 Landau theory—second-order transitions

　　4.5.4 Thermal capacity in the Landau model

　　4.5.5 Ferromagnet in a magnetic field

　4.6 Ferroelectricity

　　4.6.1 Description of the phenomenon

　　4.6.2 Landau free energy

　　4.6.3 Second-order case

　　4.6.4 First-order case

　　4.6.5 Entropy and latent heat at the transition

　　4.6.6 Soft modes

　4.7 Binary Mixtures

　　4.7.1 Basic ideas

　　4.7.2 Model calculation

　　4.7.3 System energy

　　4.7.4 Entropy

　　4.7.5 Free energy

　　4.7.6 Phase separation—the lever rule

　　4.7.7 Phase separation curve—the binodal

　　4.7.8 The spinodal curve

　　4.7.9 Entropy in the ordered phase

　　4.7.10 Thermal capacity in the ordered phase

　　4.7.11 Order of the transition and the critical point

　　4.7.12 The critical exponent β

　4.8 Quantum Phase Transitions

　　4.8.1 Introduction

　　4.8.2 The transverse Ising model

　　4.8.3 Revision of mean field Ising model

　　4.8.4 Application of a transverse field

　　4.8.5 Transition temperature

　　4.8.6 Quantum critical behaviour

　　4.8.7 Dimensionality and critical exponents

　4.9 Retrospective

　　4.9.1 The existence of order

　　4.9.2 Validity of mean field theory

　　4.9.3 Features of different phase transition models

5 Fluctuations and Dynamics

　5.1 Fluctuations

　　5.1.1 Probability distribution functions

　　5.1.2 Mean behaviour of fluctuations

　　5.1.3 The autocorrelation function

　　5.1.4 The correlation time

　5.2 Brownian Motion

　　5.2.1 Kinematics of a Brownian particle

　　5.2.2 Short time limit

　　5.2.3 Long time limit

　5.3 Langevin's Equation

　　5.3.1 Introduction

　　5.3.2 Separation of forces

　　5.3.3 The Langevin equation

　　5.3.4 Mean square velocity and equipartition

……