Ⅰ.THE FUNDAMENTAL PRINCIPLES OF STATISTICAL PHYSICS 1
1.Statistical distributions 1
2.Statistical independence 6
3.Liouville’s theorem 9
4.The significance of energy 11
5.The statistical matrix 14
6.Statistical distributions in quantum statistics 21
7.Entropy 23
8.The law of increase of entropy 29
Ⅱ.THERMODYNAMIC QUANTITIES 34
9.Temperature 34
10.Macroscopic motion 36
11.Adiabatic processes 38
12.Pressure 41
13.Work and quantity of heat 44
14.The heat function 47
15.The free energy and the thermodynamic potential 48
16.Relations between the derivatives of thermodynamic quantities 51
17.The thermodynamic scale of temperature 55
18.The Joule-Thomson process 56
19.Maximum work 57
20.Maximum work done by a body in an external medium 59
21.Thermodynamic inequalities 63
22.Le Chatelier’s principle 65
23.Nernst’s theorem 68
24.The dependence of the thermodynamic quantities on the number of particles 70
25.Equilibrium of a body in an external field 73
26.Rotating bodies 74
27.Thermodynamic relations in the relativistic region 76
Ⅲ.THE GIBBS DISTRIBUTION 79
28.The Gibbs distribution 79
29.The Maxwellian distribution 82
30.The probability distribution for an oscillator 87
31.The free energy in the Gibbs distribution 91
32.Thermodynamic perturbation theory 95
33.Expansion in powers of h 98
34.The Gibbs distribution for rotating bodies 104
35.The Gibbs distribution for a variable number of particles 106
36.The derivation of the thermodynamic relations from the Gibbs distribution 109
Ⅳ.IDEAL GASES 111
37.The Boltzmann distribution 111
38.The Boltzmann distribution in classical statistics 113
39.Molecular collisions 115
40.Ideal gases not in equilibrium 118
41.The free energy of an ideal Boltzmann gas 120
42.The equation of state of an ideal gas 121
43.Ideal gases with constant specific heat 125
44.The law of equipartition 129
45.Monatomic ideal gases 132
46.Monatomic gases.The effect of the electronic angular momentum 135
47.Diatomic gases with molecules of unlike atoms.Rotation of molecules 137
48.Diatomic gases with molecules of like atoms.Rotation of molecules 141
49.Diatomic gases.Vibrations of atoms 143
50.Diatomic gases.The effect of the electronic angular momentum 146
51.Polyatomic gases 148
52.Magnetism of gases 152
Ⅴ.THE FERMI AND BOSE DISTRIBUTIONS 158
53.The Fermi distribution 158
54.The Bose distribution 159
55.Fermi and Bose gases not in equilibrium 160
56.Fermi and Bose gases of elementary particles 162
57.A degenerate electron gas 166
58.The specific heat of a degenerate electron gas 168
59.Magnetism of an electron gas.Weak fields 171
60.Magnetism of an electron gas.Strong fields 175
61.A relativistic degenerate electron gas 178
62.A degenerate Bose gas 180
63.Black-body radiation 183
Ⅵ.SOLIDS 191
64.Solids at low temperatures 191
65.Solids at high temperatures 195
66.Debye’s interpolation formula 198
67.Thermal expansion of solids 201
68.Highly anisotropic crystals 203
69.Crystal lattice vibrations 207
70.Number density of vibrations 211
71.Phonons 215
72.Phonon creation and annihilation operators 218
73.Negative temperatures 221
Ⅶ.NON-IDEAL GASES 225
74.Deviations of gases from the ideal state 225
75.Expansion in powers of the density 230
76.Van der Waals’ formula 232
77.Relationship of the virial coefficient and the scattering amplitude 236
78.Thermodynamic quantities for a classical plasma 239
79.The method of correlation functions 243
80.Thermodynamic quantities for a degenerate plasma 245
Ⅷ.PHASE EQUILIBRIUM 251
81.Conditions of phase equilibrium 251
82.The Clapeyron-Clausius formula 255
83.The critical point 257
84.The law of corresponding states 260
Ⅸ.SOLUTIONS 263
85.Systems containing different particles 263
86.The phase rule 264
87.Weak solutions 265
88.Osmotic pressure 267
89.Solvent phases in contact 268
90.Equilibrium with respect to the solute 271
91.Evolution of heat and change of volume on dissolution 274
92.Solutions of strong electrolytes 277
93.Mixtures of ideal gases 279
94.Mixtures of isotopes 281
95.Vapour pressure over concentrated solutions 283
96.Thermodynamic inequalities for solutions 286
97.Equilibrium curves 289
98.Examples of phase diagrams 295
99.Intersection of singular curves on the equilibrium surface 300
100.Gases and liquids 301
Ⅹ.CHEMICAL REACTIONS 305
101.The condition for chemical equilibrium 305
102.The law of mass action 306
103.Heat of reaction 310
104.Ionisation equilibrium 313
105.Equilibrium with respect to pair production 315
Ⅺ.PROPERTIES OF MATTER AT VERY HIGH DENSITY 317
106.The equation of state of matter at high density 317
107.Equilibrium of bodies of large mass 320
108.The energy of a gravitating body 327
109.Equilibrium of a neutron sphere 329
Ⅻ.FLUCTUATIONS 333
110.The Gaussian distribution 333
111.The Gaussian distribution for more than one variable 335
112.Fluctuations of the fundamental thermodynamic quantities 338
113.Fluctuations in an ideal gas 345
114.Poisson’s formula 347
115.Fluctuations in solutions 349
116.Spatial correlation of density fluctuations 350
117.Correlation of density fluctuations in a degenerate gas 354
118.Correlations of fluctuations in time 359
119.Time correlations of the fluctuations of more than one variable 363
120.The symmetry of the kinetic coefficients 365
121.The dissipative function 368
122.Spectral resolution of fluctuations 371
123.The generalised susceptibility 377
124.The fluctuation-dissipation theorem 384
125.The fluctuation-dissipation theorem for more than one variable 389
126.The operator form of the generalised susceptibility 393
127.Fluctuations in the curvature of long molecules 396
ⅩⅢ.THE SYMMETRY OF CRYSTALS 401
128.Symmetry elements of a crystal lattice 401
129.The Bravais lattice 403
130.Crystal systems 405
131.Crystal classes 409
132.Space groups 411
133.The reciprocal lattice 413
134.Irreducible representations of space groups 416
135.Symmetry under time reversal 422
136.Symmetry properties of normal vibrations of a crystal lattice 427
137.Structures periodic in one and two dimensions 432
138.The correlation function in two-dimensional systems 436
139.Symmetry with respect to orientation of molecules 438
140.Nematic and cholesteric liquid crystals 440
141.Fluctuations in liquid crystals 442
ⅩⅣ.PHASE TRANSITIONS OF THE SECOND KIND AND CRITICAL PHENOMENA 446
142.Phase transitions of the second kind 446
143.The discontinuity of specific heat 451
144.Effect of an external field on a phase transition 456
145.Change in symmetry in a phase transition of the second kind 459
146.Fluctuations of the order parameter 471
147.The effective Hamiltonian 478
148.Critical indices 483
149.Scale invariance 489
150.Isolated and critical points of continuous transition 493
151.Phase transitions of the second kind in a two-dimensional lattice 498
152.Van der Waals theory of the critical point 506
153.Fluctuation theory of the critical point 511
ⅩⅤ.SURFACES 517
154.Surface tension 517
155.Surface tension of crystals 520
156.Surface pressure 522
157.Surface tension of solutions 524
158.Surface tension of solutions of strong electrolytes 526
159.Adsorption 527
160.Wetting 529
161.The angle of contact 531
162.Nucleation in phase transitions 533
163.The impossibility of the existence of phases in one-dimensional systems 537
Index 539