| Preface to the third Russian edition |
|
xiii | |
| From the prefaces to previous Russian editions |
|
xv | |
| Notation |
|
xvii | |
| I. THE FUNDAMENTAL PRINCIPLES OF STATISTICAL PHYSICS |
|
|
Statistical distributions |
|
|
1 | (5) |
|
|
|
6 | (3) |
|
|
|
9 | (2) |
|
The significance of energy |
|
|
11 | (3) |
|
|
|
14 | (7) |
|
Statistical distributions in quantum statistics |
|
|
21 | (2) |
|
|
|
23 | (6) |
|
The law of increase of entropy |
|
|
29 | (5) |
| II. THERMODYNAMIC QUANTITIES |
|
|
|
|
34 | (2) |
|
|
|
36 | (2) |
|
|
|
38 | (3) |
|
|
|
41 | (3) |
|
Work and quantity of heat |
|
|
44 | (3) |
|
|
|
47 | (1) |
|
The free energy and the thermodynamic potential |
|
|
48 | (3) |
|
Relations between the derivatives of thermodynamic quantities |
|
|
51 | (4) |
|
The thermodynamic scale of temperature |
|
|
55 | (1) |
|
The Joule-Thomson process |
|
|
56 | (1) |
|
|
|
57 | (2) |
|
Maximum work done by a body in an external medium |
|
|
59 | (4) |
|
Thermodynamic inequalities |
|
|
63 | (2) |
|
|
|
65 | (3) |
|
|
|
68 | (2) |
|
The dependence of the thermodynamic quantities on the number of particles |
|
|
70 | (3) |
|
Equilibrium of a body in an external field |
|
|
73 | (1) |
|
|
|
74 | (2) |
|
Thermodynamic relations in the relativistic region |
|
|
76 | (3) |
| III. THE GIBBS DISTRIBUTION |
|
|
|
|
79 | (3) |
|
The Maxwellian distribution |
|
|
82 | (5) |
|
The probability distribution for an oscillator |
|
|
87 | (4) |
|
The free energy in the Gibbs distribution |
|
|
91 | (4) |
|
Thermodynamic perturbation theory |
|
|
95 | (3) |
|
|
|
98 | (6) |
|
The Gibbs distribution for rotating bodies |
|
|
104 | (2) |
|
The Gibbs distribution for a variable number of particles |
|
|
106 | (3) |
|
The derivation of the thermodynamic relations from the Gibbs distribution |
|
|
109 | (2) |
| IV. IDEAL GASES |
|
|
The Boltzmann distribution |
|
|
111 | (2) |
|
The Boltzmann distribution in classical statistics |
|
|
113 | (2) |
|
|
|
115 | (3) |
|
Ideal gases not in equilibrium |
|
|
118 | (2) |
|
The free energy of an ideal Boltzmann gas |
|
|
120 | (1) |
|
The equation of state of an ideal gas |
|
|
121 | (4) |
|
Ideal gases with constant specific heat |
|
|
125 | (4) |
|
|
|
129 | (3) |
|
|
|
132 | (3) |
|
Monatomic gases. The effect of the electronic angular momentum |
|
|
135 | (2) |
|
Diatomic gases with molecules of unlike atoms. Rotation of molecules |
|
|
137 | (4) |
|
Diatomic gases with molecules of like atoms. Rotation of molecules |
|
|
141 | (2) |
|
Diatomic gases. Vibrations of atoms |
|
|
143 | (3) |
|
Diatomic gases. The effect of the electronic angular momentum |
|
|
146 | (2) |
|
|
|
148 | (4) |
|
|
|
152 | (6) |
| V. THE FERMI AND BOSE DISTRIBUTIONS |
|
|
|
|
158 | (1) |
|
|
|
159 | (1) |
|
Fermi and Bose gases not in equilibrium |
|
|
160 | (2) |
|
Fermi and Bose gases of elementary particles |
|
|
162 | (4) |
|
A degenerate electron gas |
|
|
166 | (2) |
|
The specific heat of a degenerate electron gas |
|
|
168 | (3) |
|
Magnetism of an electron gas. Weak fields |
|
|
171 | (4) |
|
Magnetism of an electron gas. Strong fields |
|
|
175 | (3) |
|
A relativistic degenerate electron gas |
|
|
178 | (2) |
|
|
|
180 | (3) |
|
|
|
183 | (8) |
| VI. SOLIDS |
|
|
Solids at low temperatures |
|
|
191 | (4) |
|
Solids at high temperatures |
|
|
195 | (3) |
|
Debye's interpolation formula |
|
|
198 | (3) |
|
Thermal expansion of solids |
|
|
201 | (2) |
|
Highly anisotropic crystals |
|
|
203 | (4) |
|
Crystal lattice vibrations |
|
|
207 | (4) |
|
Number density of vibrations |
|
|
211 | (4) |
|
|
|
215 | (3) |
|
Phonon creation and annihilation operators |
|
|
218 | (3) |
|
|
|
221 | (4) |
| VII. NON-IDEAL GASES |
|
|
Deviations of gases from the ideal state |
|
|
225 | (5) |
|
Expansion in powers of the density |
|
|
230 | (2) |
|
|
|
232 | (4) |
|
Relationship of the virial coefficient and the scattering amplitude |
|
|
236 | (3) |
|
Thermodynamic quantities for a classical plasma |
|
|
239 | (4) |
|
The method of correlation functions |
|
|
243 | (2) |
|
Thermodynamic quantities for a degenerate plasma |
|
|
245 | (6) |
| VIII. PHASE EQUILIBRIUM |
|
|
Conditions of phase equilibrium |
|
|
251 | (4) |
|
The Clapeyron-Clausius formula |
|
|
255 | (2) |
|
|
|
257 | (3) |
|
The law of corresponding states |
|
|
260 | (3) |
| IX. SOLUTIONS |
|
|
Systems containing different particles |
|
|
263 | (1) |
|
|
|
264 | (1) |
|
|
|
265 | (2) |
|
|
|
267 | (1) |
|
Solvent phases in contact |
|
|
268 | (3) |
|
Equilibrium with respect to the solute |
|
|
271 | (3) |
|
Evolution of heat and change of volume on dissolution |
|
|
274 | (3) |
|
Solutions of strong electrolytes |
|
|
277 | (2) |
|
|
|
279 | (2) |
|
|
|
281 | (2) |
|
Vapour pressure over concentrated solutions |
|
|
283 | (3) |
|
Thermodynamic inequalities for solutions |
|
|
286 | (3) |
|
|
|
289 | (6) |
|
Examples of phase diagrams |
|
|
295 | (5) |
|
Intersection of singular curves on the equilibrium surface |
|
|
300 | (1) |
|
|
|
301 | (4) |
| X. CHEMICAL REACTIONS |
|
|
The condition for chemical equilibrium |
|
|
305 | (1) |
|
|
|
306 | (4) |
|
|
|
310 | (3) |
|
|
|
313 | (2) |
|
Equilibrium with respect to pair production |
|
|
315 | (2) |
| XI. PROPERTIES OF MATTER AT VERY HIGH DENSITY |
|
|
The equation of state of matter at high density |
|
|
317 | (3) |
|
Equilibrium of bodies of large mass |
|
|
320 | (7) |
|
The energy of a gravitating body |
|
|
327 | (2) |
|
Equilibrium of a neutron sphere |
|
|
329 | (4) |
| XII. FLUCTUATIONS |
|
|
The Gaussian distribution |
|
|
333 | (2) |
|
The Gaussian distribution for more than one variable |
|
|
335 | (3) |
|
Fluctuations of the fundamental thermodynamic quantities |
|
|
338 | (7) |
|
Fluctuations in an ideal gas |
|
|
345 | (2) |
|
|
|
347 | (2) |
|
Fluctuations in solutions |
|
|
349 | (1) |
|
Spatial correlation of density fluctuations |
|
|
350 | (4) |
|
Correlation of density fluctuations in a degenerate gas |
|
|
354 | (5) |
|
Correlations of fluctuations in time |
|
|
359 | (4) |
|
Time correlations of the fluctuations of more than one variable |
|
|
363 | (2) |
|
The symmetry of the kinetic coefficients |
|
|
365 | (3) |
|
|
|
368 | (3) |
|
Spectral resolution of fluctuations |
|
|
371 | (6) |
|
The generalised susceptibility |
|
|
377 | (7) |
|
The fluctuation-dissipation theorem |
|
|
384 | (5) |
|
The fluctuation-dissipation theorem for more than one variable |
|
|
389 | (4) |
|
The operator form of the generalised susceptibility |
|
|
393 | (3) |
|
Fluctuations in the curvature of long molecules |
|
|
396 | (5) |
| XIII. THE SYMMETRY OF CRYSTALS |
|
|
Symmetry elements of a crystal lattice |
|
|
401 | (2) |
|
|
|
403 | (2) |
|
|
|
405 | (4) |
|
|
|
409 | (2) |
|
|
|
411 | (2) |
|
|
|
413 | (3) |
|
Irreducible representations of space groups |
|
|
416 | (6) |
|
Symmetry under time reversal |
|
|
422 | (5) |
|
Symmetry properties of normal vibrations of a crystal lattice |
|
|
427 | (5) |
|
Structures periodic in one and two dimensions |
|
|
432 | (4) |
|
The correlation function in two-dimensional systems |
|
|
436 | (2) |
|
Symmetry with respect to orientation of molecules |
|
|
438 | (2) |
|
Nematic and cholesteric liquid crystals |
|
|
440 | (2) |
|
Fluctuations in liquid crystals |
|
|
442 | (4) |
| XIV. PHASE TRANSITIONS OF THE SECOND KIND AND CRITICAL PHENOMENA |
|
|
Phase transitions of the second kind |
|
|
446 | (5) |
|
The discontinuity of specific heat |
|
|
451 | (5) |
|
Effect of an external field on a phase transition |
|
|
456 | (3) |
|
Change in symmetry in a phase transition of the second kind |
|
|
459 | (12) |
|
Fluctuations of the order parameter |
|
|
471 | (7) |
|
The effective Hamiltonian |
|
|
478 | (5) |
|
|
|
483 | (6) |
|
|
|
489 | (4) |
|
Isolated and critical points of continuous transition |
|
|
493 | (5) |
|
Phase transitions of the second kind in a two-dimensional lattice |
|
|
498 | (8) |
|
Van der Waals theory of the critical point |
|
|
506 | (5) |
|
Fluctuation theory of the critical point |
|
|
511 | (6) |
| XV. SURFACES |
|
|
|
|
517 | (3) |
|
Surface tension of crystals |
|
|
520 | (2) |
|
|
|
522 | (2) |
|
Surface tension of solutions |
|
|
524 | (2) |
|
Surface tension of solutions of strong electrolytes |
|
|
526 | (1) |
|
|
|
527 | (2) |
|
|
|
529 | (2) |
|
|
|
531 | (2) |
|
Nucleation in phase transitions |
|
|
533 | (4) |
|
The impossibility of the existence of phases in one-dimensional systems |
|
|
537 | (2) |
| Index |
|
539 | |