Statistical Theory of Heat: Nonequilibrium Phenomena

This book provides an integrated presentation of nonequilibrium statistical physics based on the methods of correlation functions and memory kernels. The relation between this approach and other, earlier methods such as kinetic equations, transport equations and Onsager's approach is discussed in detail. Classical results of kinetic and transport theory are treated thoroughly, together with more recent results on hydrodynamic long time tails, dynamical scaling laws for critical phenomena and electron localization in random potentials. The growing interest in nonlinear phenomena is catered for by several chapters on related problems: a general microscopic nonlinear response theory is presented; phenomenological nonlinear equations are discussed with respect to their relations with microscopic theory and their applications in chemical reactions, hydrodynamics and "chaos"; microscopic nonlinear theory is used to calculate kinetic coefficients of nonlinear phenomenological theories such as transport theory and chemical reactions.

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.