Statistical Theory of Heat

I Correlation Functions and Kinetic Equations.- 1. Introduction.- 2. General Equations of Motion of Statistical Physics.- 2.1 Quantum Statistics.- 2.2 Classical Statistics.- 2.3 Approximations.- Problems.- 3. Small Amplitude Perturbation Theory (Linear Response).- Problems.- 4. Brownian Motion (Relaxator)*.- Problems.- 5. Brownian Motion (Oscillator)*.- Problems.- 6. Dispersion Relations and Spectral Representations.- Problems.- 7. Symmetry Properties of Correlation Functions.- Problems.- 8. Detailed Balance, Fluctuations and Dissipation.- Problems.- 9. Scattering of Particles and Light**.- Problems.- 10. Energy Dissipation, Detailed Balance and Passivity.- 10.1 The Response of Conserved Quantities to External Forces.- 10.2 Energy Dissipation and Passivity.- Problems.- 11. The High-Frequency Behaviour of Response Functions.- Problems.- 12. The Low-Frequency Behaviour of Response Functions.- Problems.- 13. Stochastic Forces, Langevin Equation.- 13.1 The Subtraction Method (Langevin).- 13.2 The Projection Method (Zwanzig and Mori).- Problems.- 14. Brownian Motion: Langevin Equation*.- Problems.- 15. Nonlinear Response Theory.- 15.1 The General Initial Value Case.- 15.2 Low-Frequency Perturbation Theory.- Problems.- 16. The Increase of Entropy and Irreversibility.- 16.1 General.- 16.2 Linear Response.- 16.3 Low-Frequency Response.- Problems.- 17. The Increase of Entropy: A Critical Discussion**.- 17.1 Maxwell’s Demon.- 17.2 Gibbs’Ink Parable.- 17.3 Zermél;lo’s Recurrence Paradox.- 17.4 Loschmidt’s Reversibility Objection.- Problems.- II Irreversible Thermodynamics.- 18. The Nyquist Formula.- Problems.- 19. Thermomechanical Effects.- 19.1 Diffusion and the Mechanocaloric Effect (?T = 0).- 19.2 Heat Diffusion and Thermomechanical Pressure Difference ($$\dot N$$ = 0).- Problems.- 20. Diffusion and Thermodiffusion.- Problems.- 21. Thermoelectric Effects.- Problems.- 22. Chemical Reactions.- Problems.- 23. Typical Time Evolutions of Simple Chemical Reactions.- 23.1 Zero-Order Reactions.- 23.2 First-Order Reactions.- 23.3 Second-Order Reactions.- 23.4 Third-Order Reactions.- Problems.- 24. Coupled Nonlinear Reactions.- 24.1 Nonequilibrium Phase Transitions.- 24.2 Kinetic Oscillations.- 24.3 “Chaos”.- Problems.- 25. Chemical Fluctuations.- Problems.- 26. Sticking, Desorption, Condensation and Evaporation.- Problems.- 27. Nucleation.- Problems.- 28. The Oscillator with Mechanical and Thermal Attenuation*.- Problems.- 29. Hydrodynamics.- Problems.- 30. Hydrodynamic Long-Time Tails.- Problems.- 31. Matter in Electromagnetic Fields.- Problems.- 32. Rate Equations (Master Equation, Stosszahlansatz).- Problems.- 33. Kinetic Transport Equations.- Problems.- 34. The Dynamic Conductivity in the Relaxation Time Model.- 34.1 Longitudinal Excitations.- 34.2 Transverse Excitations.- 34.3 Discussion of ?l(k,?) and ?t(k,?).- 34.4 Quantum Corrections.- Problems.- 35. Zero Sound.- Problems.- 36. The Fokker-Planck Approximation.- Problems.- 37. Brownian Motion and Diffusion*.- Problems.- 38. Fokker-Planck and Langevin Equations.- 39. Transport Equations in the Hydrodynamic Regime.- 39.1 The Hydrodynamic Approximation.- 39.2 Diffusion of Particles and Heat.- 39.3 The Viscosities.- Problems.- 40. The Minimum Entropy Production Variational Principle.- 40.1 The Principle of Minimum Entropy Production.- 40.2 The Classical Boltzmann Gas.- 40.3 The Electron-Phonon System.- 40.4 Fermi Liquids.- Problems.- III Calculation of Kinetic Coefficients.- 41. Approximation Methods.- 42. Correlation Functions for Single-Particle Problems.- 42.1 General.- 42.2 Impurity Conduction (Greenwood Formula).- Problems.- 43. Perturbation Theory for Impurity Conduction.- Problems.- 44. Electron-Phonon Conduction.- Problems.- 45. Mode-Coupling Theory for Impurity Conduction.- 45.1 Particle Diffusion and Current Relaxation.- 45.2 Backscattering Effects.- 45.3 Self-Consistency Relations.- Problems.- 46. Electron Localization.- 46.1 Breakdown of Perturbation Theory.- 46.2 Localization and Nonergodicity.- 46.3 Critical Behaviour and Scaling Laws.- Problems.- 47. Localization and Quantum Interference*.- 48. Scaling Laws for Dynamic Critical Phenomena.- 48.1 General.- 48.2 The Lambda Transition in Liquid Helium.- Problems.- 49. Applications of Dynamic Scaling Laws.- 49.1 Isotropic Ferromagnets.- 49.2 Uniaxial Antiferromagnets, Structural Phase Transitions.- 49.3 Anisotropic Ferromagnets.- 49.4 Liquid-Gas Transition.- 50. Mode-Coupling Theory for Dynamic Critical Phenomena.- 51. Broken Symmetry and Low-Frequency Modes**.- 52. Collision Rates.- 52.1 Perturbation Theory.- 52.2 Impurity Scattering.- 52.3 Chemical Reaction Rates.- Problems.- 53. Many-Body Effects in Collision Rates.- Problems.- References.