Statistical Physics by Tony Guénault

1 Basic ideas 1
1.1 The macrostate 1
1.2 Microstates 2
1.3 The averaging postulate 3
1.4 Distributions 4
1.5 The statistical method in outline 6
1.6 A model example 7
1.7 Statistical entropy and microstates 10
1.8 Summary 11
2 Distinguishable particles 13
2.1 The Thermal Equilibrium Distribution 14
2.2 What are α and β? 17
2.3 A statistical definition of temperature 18
2.4 The boltzmann distribution and the partition function 21
2.5 Calculation of thermodynamic functions 22
2.6 Summary 23
3 Two examples 25
3.1 A Spin- 1
2 solid 25
3.2 Localized harmonic oscillators 36
3.3 Summary 40
4 Gases: the density of states 43
4.1 Fitting waves into boxes 43
4.2 Other information for statistical physics 47
4.3 An example – helium gas 48
4.4 Summary 49
5 Gases: the distributions 51
5.1 Distribution in groups 51
5.2 Identical particles – fermions and bosons 53
5.3 Counting microstates for gases 55
5.4 The three distributions 58
5.5 Summary 61
6 Maxwell–Boltzmann gases 63
6.1 The validity of the Maxwell–Boltzmann limit 63
6.2 The Maxwell–Boltzmann distribution of speeds 65
6.3 The connection to thermodynamics 68
6.4 Summary 71
7 Diatomic gases 73
7.1 Energy contributions in diatomic gases 73
7.2 Heat capacity of a diatomic gas 75
7.3 The heat capacity of hydrogen 78
7.4 Summary 81
8 Fermi–Dirac gases 83
8.1 Properties of an ideal Fermi–Dirac gas 84
8.2 Application to metals 91
8.3 Application to helium-3 92
8.4 Summary 95
9 Bose–Einstein gases 97
9.1 Properties of an ideal Bose–Einstein gas 97
9.2 Application to helium-4 101
9.3 Phoney bosons 104
9.4 A note about cold atoms 109
9.5 Summary 109
10 Entropy in other situations 111
10.1 Entropy and disorder 111
10.2 An assembly at fixed temperature 114
10.3 Vacancies in solids 116
11 Phase transitions 119
11.1 Types of phase transition 119
11.2 Ferromagnetism of a spin- 1
2 solid 120
11.3 Real ferromagnetic materials 126
11.4 Order–disorder transformations in alloys 127
12 Two new ideas 129
12.1 Statics or dynamics? 129
12.2 Ensembles – a larger view 132
13 Chemical thermodynamics 137
13.1 Chemical potential revisited 137
13.2 The grand canonical ensemble 139
13.3 Ideal gases in the grand ensemble 141
13.4 Mixed systems and chemical reactions 146
14 Dealing with interactions 153
14.1 Electrons in metals 154
14.2 Liquid helium-3: A Fermi liquid 158
14.3 Liquid helium-4: A Bose liquid? 163
14.4 Real imperfect gases 164
15 Statistics under extreme conditions 169
15.1 Superfluid states in Fermi–Dirac systems 169
15.2 Statistics in astrophysical systems 174
Appendix A Some elementary counting problems 181
Appendix B Some problems with large numbers 183
Appendix C Some useful integrals 187
Appendix D Some useful constants 191
Appendix E Exercises 193
Appendix F Answers to exercises 199
Index 201