Statistical Mechanics Of Nonequilibrium Processes Statistical Mechanics Of Nonequilibrium Processes Volume 2

This is the second part of a two-volume textbook on the modern statistical theory of nonequilibrium processes. The general method of nonequilibrium statistical ensembles developed in the first volume is applied to various problems in linear response theory, relaxation phenomena, hydrodynamics, and the dynamical theory of fluctuations. Some active areas of research are considered, including relaxation processes in highly nonequilibrium systems, kinetic processes in lasers, nonequilibrium many-particle correlations in the Green’s function formalism, superfluid statistical hydrodynamics, large-scale fluctuations in nonequilibrium systems, and statistical mechanics of turbulence. Exercises and problems for readers are also included. The book is self-contained and accessible to students having heard the standard course in statistical physics. It is also of interest for specialists working in solid state physics, chemical physics, and physics of plasma and fluids.

The structure of the theory ofthermodynamics has changed enormously since its inception in the middle of the nineteenth century. Shortly after Thomson and Clausius enunciated their versions of the Second Law, Clausius, Maxwell, and Boltzmann began actively pursuing the molecular basis of thermo dynamics, work that culminated in the Boltzmann equation and the theory of transport processes in dilute gases. Much later, Onsager undertook the elucidation of the symmetry oftransport coefficients and, thereby, established himself as the father of the theory of nonequilibrium thermodynamics. Com bining the statistical ideas of Gibbs and Langevin with the phenomenological transport equations, Onsager and others went on to develop a consistent statistical theory of irreversible processes. The power of that theory is in its ability to relate measurable quantities, such as transport coefficients and thermodynamic derivatives, to the results of experimental measurements. As powerful as that theory is, it is linear and limited in validity to a neighborhood of equilibrium. In recent years it has been possible to extend the statistical theory of nonequilibrium processes to include nonlinear effects. The modern theory, as expounded in this book, is applicable to a wide variety of systems both close to and far from equilibrium. The theory is based on the notion of elementary molecular processes, which manifest themselves as random changes in the extensive variables characterizing a system. The theory has a hierarchical character and, thus, can be applied at various levels of molecular detail.

This book aims to provide a compact and unified introduction to the most important aspects in the physics of non-equilibrium systems. It first introduces stochastic processes and some modern tools and concepts that have proved their usefulness to deal with non-equilibrium systems from a purely probabilistic angle. The aim is to show the important role played by fluctuations in far-from-equilibrium situations, where noise can promote order and organization, switching among non-equilibrium states, etc. The second part adopts a more historical perspective, retracing the first steps taken from the purely thermodynamic as well as from the kinetic points of view to depart (albeit slightly) from equilibrium. The third part revisits the path outlined in the first one, but now undertakes the mesoscopic description of extended systems, where new phenomena (patterns, long-range correlations, scaling far from equilibrium, etc.) are observed. This book is a revised and extended version of an earlier edition published in 1994. It includes topics of current research interest in far-from-equilibrium situations like noise-induced phenomena and free energy-like functionals, surface growth and roughening, etc. It can be used as an advanced textbook by graduate students in physics. It also covers topics of current interest in other disciplines and interdisciplinary approaches in engineering, biophysics, and economics, among others. The level of detail in the book is enough to capture the interest of the reader and facilitate the path to more learning by exploring the modern research literature provided. At the same time, the book is also complete enough to be self-contained for those readers who just need an overview of the subject.

"There is a symbiotic relationship between theoretical nonequilibrium statistical mechanics on the one hand and the theory and practice of computer simulation on the other. Sometimes, the initiative for progress has been with the pragmatic requirements of computer simulation and at other times, the initiative has been with the fundamental theory of nonequilibrium processes. This book summarises progress in this field up to 1990"--Publisher's description.

This is the first part of a two-volume textbook on the modern statistical theory of nonequilibrium processes. In distinction to currently available textbooks and monographs on this subject, the presentation of a wide range of nonequilibrium phenomena in many-particle systems is based on the unified approach which is a natural extension of the method of Gibbs ensembles to the nonequilibrium case. The general method of nonequilibrium ensembles is applied to describe kinetic processes in classical and quantum systems. In addition to standard examples, topical problems of the modern kinetic theory are considered, including many-particle effects in classical kinetics, non-Markovian kinetic equations for plasmas, and quantum kinetic processes in the presence of strong external fields. Exercises and problems for readers are also included. The book is self-contained and accessible to students having read the standard course in statistical physics. It is also of interest for specialists working in solid state physics, chemical physics, and physics of plasma and fluids.

This volume of Statistical Physics consititutes the second part of Statistical Physics (Springer Series in Solid-State Science, Vols. 30, 31) and is devoted to nonequilibrium theories of statistical mechanics. We start with an intro duction to the stochastic treatment of Brownian motion and then proceed to general problems involved in deriving a physical process from an underlying more basic process. Relaxation from nonequilibrium to equilibrium states and the response of a system to an external disturbance form the central problems of nonequilibrium statistical mechanics. These problems are treated both phenomenologically and microscopically along the lines of re cent developments. Emphasis is placed on fundamental concepts and methods rather than on applications which are too numerous to be treated exhaustively within the limited space of this volume. For information on the general aim of this book, the reader is referred to the Foreword. For further reading, the reader should consult the bibliographies, although these are not meant to be exhaustive.