Preface -- 1 Basic principles of statistics -- 1.1 Introduction -- 1.2 Distribution functions -- 1.3 Statistical independence -- 1.4 Liouville theorem -- 1.5 Role of energy, microcanonical distribution -- 1.6 Partial distribution functions -- 1.7 Density matrix -- 1.7.1 Pure ensemble -- 1.7.2 Mixed ensemble -- 1.8 Quantum Liouville equation -- 1.9 Microcanonical distribution in quantum statistics -- 1.10 Partial density matrices -- 1.11 Entropy -- 1.11.1 Gibbs entropy. Entropy and probability -- 1.11.2 The law of entropy growth -- 2 Gibbs distribution -- 2.1 Canonical distribution -- 2.2 Maxwell distribution -- 2.3 Free energy from Gibbs distribution -- 2.4 Gibbs distribution for systems with varying number of particles -- 2.5 Thermodynamic relations from Gibbs distribution -- 3 Classical ideal gas -- 3.1 Boltzmann distribution -- 3.2 Boltzmann distribution and classical statistics -- 3.3 Nonequilibrium ideal gas -- 3.4 Free energy of Boltzmann gas -- 3.5 Equation of state of Boltzmann gas -- 3.6 Ideal gas with constant specific heat -- 3.7 Equipartition theorem -- 3.8 One-atom ideal gas -- 4 Quantum ideal gases -- 4.1 Fermi distribution -- 4.2 Bose distribution -- 4.3 Nonequilibrium Fermi and Bose gases -- 4.4 General properties of Fermi and Bose gases -- 4.5 Degenerate gas of electrons -- 4.6 Relativistic degenerate electron gas -- 4.7 Specific heat of a degenerate electron gas -- 4.8 Magnetism of an electron gas in weak fields -- 4.9 Magnetism of an electron gas in high fields -- 4.10 Degenerate Bose gas -- 4.11 Statistics of photons -- 5 Condensed matter -- 5.1 Solid state at low temperature -- 5.2 Solid state at high temperature -- 5.3 Debye theory -- 5.4 Quantum Bose liquid -- 5.5 Superfluidity -- 5.6 Phonons in a Bose liquid -- 5.7 Degenerate interacting Bose gas -- 5.8 Fermi liquids -- 5.9 Electron liquid in metals.

6 Superconductivity -- 6.1 Cooper instability -- 6.2 Energy spectrum of superconductors -- 6.3 Thermodynamics of superconductors -- 6.4 Coulomb repulsion -- 6.5 Ginzburg-Landau theory -- 7 Fluctuations -- 7.1 Gaussian distribution -- 7.2 Fluctuations in basic physical properties -- 7.3 Fluctuations in ideal gases -- 8 Phase transitions and critical phenomena -- 8.1 Mean-field theory of magnetism -- 8.2 Quasi-averages -- 8.3 Fluctuations in the order parameter -- 8.4 Scaling -- 9 Linear response -- 9.1 Linear response to mechanical perturbation -- 9.2 Electrical conductivity and magnetic susceptibility -- 9.3 Dispersion relations -- 10 Kinetic equations -- 10.1 Boltzmann equation -- 10.2 H-theorem -- 10.3 Quantum kinetic equations -- 10.3.1 Electron-phonon interaction -- 10.3.2 Electron-electron interaction -- 11 Basics of the modern theory of many-particle systems -- 11.1 Quasiparticles and Green's functions -- 11.2 Feynman diagrams for many-particle systems -- 11.3 Dyson equation -- 11.4 Effective interaction and dielectric screening -- 11.5 Green's functions at finite temperatures -- A Motion in phase space, ergodicity and mixing -- A.1 Ergodicity -- A.2 Poincare recurrence theorem -- A.3 Instability of trajectories and mixing -- B Statistical mechanics and information theory -- B.1 Relation between Gibbs distributions and the principle of maximal information entropy -- B.2 Purging Maxwell's "demon" -- C Nonequilibrium statistical operators -- C.1 Quasi-equilibrium statistical operators -- C.2 Nonequilibrium statistical operators and quasi-averages -- Bibliography -- Index.