Statistical Physics

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) Statistical independence 6(3) Liouville's theorem 9(2) The significance of energy 11(3) The statistical matrix 14(7) Statistical distributions in quantum statistics 21(2) Entropy 23(6) The law of increase of entropy 29(5) II. THERMODYNAMIC QUANTITIES Temperature 34(2) Macroscopic motion 36(2) Adiabatic processes 38(3) Pressure 41(3) Work and quantity of heat 44(3) The heat function 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) Maximum work 57(2) Maximum work done by a body in an external medium 59(4) Thermodynamic inequalities 63(2) Le Chatelier's principle 65(3) Nernst's theorem 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) Rotating bodies 74(2) Thermodynamic relations in the relativistic region 76(3) III. THE GIBBS DISTRIBUTION 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) Expansion in powers of h 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) Molecular collisions 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) The law of equipartition 129(3) Monatomic ideal gases 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) Polyatomic gases 148(4) Magnetism of gases 152(6) V. THE FERMI AND BOSE DISTRIBUTIONS The Fermi distribution 158(1) The Bose distribution 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) A degenerate Bose gas 180(3) Black-body radiation 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) Phonons 215(3) Phonon creation and annihilation operators 218(3) Negative temperatures 221(4) VII. NON-IDEAL GASES Deviations of gases from the ideal state 225(5) Expansion in powers of the density 230(2) Van der Waal's formula 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) The critical point 257(3) The law of corresponding states 260(3) IX. SOLUTIONS Systems containing different particles 263(1) The phase rule 264(1) Weak solutions 265(2) Osmotic pressure 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) Mixtures of ideal gases 279(2) Mixtures of isotopes 281(2) Vapour pressure over concentrated solutions 283(3) Thermodynamic inequalities for solutions 286(3) Equilibrium curves 289(6) Examples of phase diagrams 295(5) Intersection of singular curves on the equilibrium surface 300(1) Gases and liquids 301(4) X. CHEMICAL REACTIONS The condition for chemical equilibrium 305(1) The law of mass action 306(4) Heat of reaction 310(3) Ionisation equilibrium 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) Poisson's formula 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) The dissipative function 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) The Bravais lattice 403(2) Crystal systems 405(4) Crystal classes 409(2) Space groups 411(2) The reciprocal lattice 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) Critical indices 483(6) Scale invariance 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 Surface tension 517(3) Surface tension of crystals 520(2) Surface pressure 522(2) Surface tension of solutions 524(2) Surface tension of solutions of strong electrolytes 526(1) Adsorption 527(2) Wetting 529(2) The angle of contact 531(2) Nucleation in phase transitions 533(4) The impossibility of the existence of phases in one-dimensional systems 537(2) Index 539