Statistical Theory of Heat, Softcover reprint of the original 1st ed. 1989 Nonequilibrium Phenomena

This text on the statistical theory of nonequilibrium phenomena grew out of lecture notes for courses on advanced statistical mechanics that were held more or less regularly at the Physics Department of the Technical University in Munich. My aim in these lectures was to incorporate various developments of many-body theory made during the last 20-30 years, in particular the correlation function approach, not just as an "extra" alongside the more "classical" results; I tried to use this approach as a unifying concept for the presentation of older as well as more recent results. I think that after so many excellent review articles and advanced treatments, correlation functions and memory kernels are as much a matter of course in nonequilibrium statistical physics as partition functions are in equilibrium theory, and should be used as such in regular courses and textbooks. The relations between correlation functions and earlier vehicles for the formulation of nonequilibrium theory such as kinetic equations, master equations, Onsager's theory, etc. , are discussed in detail in this volume. Since today there is growing interest in nonlinear phenomena I have included several chapters on related problems. There is some nonlinear response theory, some results on phenomenological nonlinear equations and some microscopic applications of the nonlinear response formalism. The main focus, however, is on the linear regime.

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.