1.Basic Principles 1.1 Introduction 1.2 A Brief Excursion into Probability Theory 1.2.1 Probability Density and Characteristic.Functions 1.2.2 The Central Limit Theorem. 1.3 Ensembles in Classical Statistics. 1.3.1 Phase Space and Distribution Functions 1.3.2 The Liouville Equation 1.4 Quantum Statistics 1.4.1 The Density Matrix for Pure and Mixed Ensembles 1.4.2 The Von Neumann Equation. *1.5 Additional Remarks *1.5.1 The Binomial and the Poisson Distributions *1.5.2 Mixed Ensembles and the Density Matrix of Subsystems Problems 2.Equilibrium Ensembles 2.1 Introductory Remarks 2.2 Microcanonical Ensembles 2.2.1 Microcanonical Distribution Functions and Density Matrices 2.2.2 The Classical Ideal Gas *2.2.3 Quantum.mechanical Harmonic Oscillators and Spin Systems 2.3 Entropy 2.3.1 General Definition 2.3.2 An Extremal Property of the Entropy 2.3.3 Entropy ofthe Microcanonical Ensemble 2.4 Temperature and Pressure 2.4.1 Systems in Contact：the Energy Distribution Function Definition of the Temperature 2.4.2 0n the Widths of the Distribution Functions of Macroscopic Quantities 2.4.3 External Parameters：Pressure 2.5 Properties of Some Non-interacting Systems 2.5.1 The Ideal Gas *2.5.2 Non-interacting Quantum Mechanical Harmonic Oscillators and Spins 2.6 The Canonical Ensemble 2.6.1 The Density Matrix 2.6.2 Examples：the Maxwell Distribution and the Barometric Pressure Formula 2.6.3 The Entropy of the Canonical Ensemble and Its Extremal Values 2.6.4 The Virial Theorem and the Equipartition Theorem 2.6.5 Thermodynamic Quantities in the Canonical Ensemble 2.6.6 Additional Properties of the Entropy 2.7 The Grand Canonical Ensemble 2.7.1 Systems with Particle Exchange 2.7.2 The Grand Canonical Density Matrix 2.7.3 Thermodynamic Quantities 2.7.4 The Grand Partition Function for the Classical Ideal Gas *2.7.5 The Grand Canonical Density Matrix in Second Quantization Problems 3.Thermodynamics 3.1 Potentials and LaWS of Equilibrium Thermodynamics 3.1.1 Definitions 3.1.2 The Legendre Transformation 3.1.3 The Gibbs-Duhem Relation in Homogeneous Systems 3.2 Derivatives of Thermodynamic Quantities 3.2.1 Definitions 3.2.2 Integrability and the Maxwell Relations 3.2.3 Jacobians 3.2.4 Examples 3.3 Fluctuations and Thermodynamic Inequalities. 3.3.1 Fluctuations 3.3.2 Inequalities 3.4 Absolute Temperature and Empirical Temperatures 3.5 Thermodynamic Processes 3.5.1 Thermodynamic Concepts 3.5.2 The Irreversible Expansion of a Gas the Gay-Lussac Experiment 3.5.3 The Statistical Foundation of Irreversibility 3.5.4 Reversible Processes 3.5.5 The Adiabatic Equation …… 3.Thermodynamics 4.Ideal Quantum Gases 5.Real Gases,Liquids,and Solutions 6.Magnetism 7.Phase Transitions,Renormalization Group Theroy,and Percolation 8.Brownian Motion,Equations of Motion and the Fokker-Planck Equations 9.The Boltzmann Equation 10.Irreversibilty and the Approach to Equilibrium Appendix Subject Index
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