Statistical physics of particles

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
1.1 Introduction......Page 13
1.2 The zeroth law......Page 14
1.3 The first law......Page 17
1.4 The second law......Page 20
1.5 Carnot engines......Page 22
1.6 Entropy......Page 25
1.7 Approach to equilibrium and thermodynamic potentials......Page 28
1.8 Useful mathematical results......Page 32
1.9 Stability conditions......Page 34
1.10 The third law......Page 38
Problems for chapter 1......Page 41
2.1 General definitions......Page 47
2.2 One random variable......Page 48
2.3 Some important probability distributions......Page 52
2.4 Many random variables......Page 55
2.5 Sums of random variables and the central limit theorem......Page 57
2.6 Rules for large numbers......Page 59
2.7 Information, entropy, and estimation......Page 62
Problems for chapter 2......Page 64
3.1 General definitions......Page 69
3.2 Liouville's theorem......Page 71
3.3 The Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy......Page 74
3.4 The Boltzmann equation......Page 77
3.5 The H-theorem and irreversibility......Page 83
3.6 Equilibrium properties......Page 87
3.7 Conservation laws......Page 90
3.8 Zeroth-order hydrodynamics......Page 94
3.9 First-order hydrodynamics......Page 96
Problems for chapter 3......Page 99
4.2 The microcanonical ensemble......Page 110
4.3 Two-level systems......Page 114
4.4 The ideal gas......Page 117
4.5 Mixing entropy and the Gibbs paradox......Page 119
4.6 The canonical ensemble......Page 122
4.7 Canonical examples......Page 125
4.8 The Gibbs canonical ensemble......Page 127
4.9 The grand canonical ensemble......Page 130
Problems for chapter 4......Page 132
5.1 The cumulant expansion......Page 138
5.2 The cluster expansion......Page 142
5.3 The second virial coefficient and van der Waals equation......Page 147
5.4 Breakdown of the van der Waals equation......Page 151
5.5 Mean-field theory of condensation......Page 153
5.6 Variational methods......Page 155
5.7 Corresponding states......Page 157
5.8 Critical point behavior......Page 158
Problems for chapter 5......Page 160
6.1 Dilute polyatomic gases......Page 168
6.2 Vibrations of a solid......Page 173
6.3 Black-body radiation......Page 179
6.4 Quantum microstates......Page 182
6.5 Quantum macrostates......Page 184
Problems for chapter 6......Page 187
7.1 Hilbert space of identical particles......Page 193
7.2 Canonical formulation......Page 196
7.3 Grand canonical formulation......Page 199
7.4 Non-relativistic gas......Page 200
7.5 The degenerate fermi gas......Page 202
7.6 The degenerate bose gas......Page 206
7.7 Superfluid He......Page 210
Problems for chapter 7......Page 214
Solutions to selected problems from Chapter 1......Page 223
Solutions to selected problems from Chapter 2......Page 236
Solutions to selected problems from Chapter 3......Page 247
Solutions to selected problems from Chapter 4......Page 268
Solutions to selected problems from Chapter 5......Page 280
Solutions to selected problems from Chapter 6......Page 297
Solutions to selected problems from Chapter 7......Page 312
Index......Page 330