영문목차
Preface ix
Thermodynamics 1
Introduction 1
The zeroth law 2
The first law 5
The second law 8
Carnot engines 10
Entropy 13
Approach to equilibrium and thermodynamic potentials 16
Useful mathematical results 20
Stability conditions 22
The third law 26
Problems 29
Probability 35
General definitions 35
One random variable 36
Some important probability distributions 40
Many random variables 43
Sums of random variables and the central limit theorem 45
Rules for large numbers 47
Information, entropy, and estimation 50
Problems 52
Kinetic theory of gases 57
General definitions 57
Liouville's theorem 59
The Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy 62
The Boltzmann equation 65
The H-theorem and irreversibility 71
Equilibrium properties 75
Conservation laws 78
Zeroth-order hydrodynamics 82
First-order hydrodynamics 84
Problems 87
Classical statistical mechanics 98
General definitions 98
The microcanonical ensemble 98
Two-level systems 102
The ideal gas 105
Mixing entropy and the Gibbs paradox 107
The canonical ensemble 110
Canonical examples 113
The Gibbs canonical ensemble 115
The grand canonical ensemble 118
Problems 120
Interacting particles 126
The cumulant expansion 126
The cluster expansion 130
The second virial coefficient and van der Waals equation 135
Breakdown of the van der Waals equation 139
Mean-field theory of condensation 141
Variational methods 143
Corresponding states 145
Critical point behavior 146
Problems 148
Quantum statistical mechanics 156
Dilute polyatomic gases 156
Vibrations of a solid 161
Black-body radiation 167
Quantum microstates 170
Quantum macrostates 172
Problems 175
Ideal quantum gases 181
Hilbert space of identical particles 181
Canonical formulation 184
Grand canonical formulation 187
Non-relativistic gas 188
The degenerate fermi gas 190
The degenerate bose gas 194
Superfluid He4 198
Problems 202
Solutions to selected problems 211(107)
Chapter 1 211
Chapter 2 224
Chapter 3 235
Chapter 4 256
Chapter 5 268
Chapter 6 285
Chapter 7 300
Index 318