Using the mathematical theory of Brownian motion, this book develops in detail the statistical basis of nonequilibrium thermodynamics. In particular, it is shown that thermodynamic criteria emerge in the limit of small thermal fluctuations and in the Gaussian limit where means and modes of the distribution coincide. The theory of Brownian motion is assumed to be a rather general and useful model of irreversible processes that are inevitably influenced by random thermal fluctuations. The unifying approach adopted allows widely applicable principles to be extracted from the analysis of particular models. The content is arranged by argument rather than by chronology. It is based on the premise that random thermal fluctuations play a decisive role in governing the evolution of nonequilibrium thermodynamic processes. They can also be viewed as a dynamic superposition of a large number of random events with the important proviso that the future evolution depends only on the present, independent of its entire past history. Using the mathematical theory of Brownian motion, this book comprehensively develops the statistical basis of nonequilibrium thermodynamics. Following a summary of the phenomenological approach to nonequilibrium thermodynamics and an introduction to Brownian motion, Professor Lavenda presents well-known theorems in nonequilibrium thermodynamics from a unifying standpoint of stochastic theory and statistical formulations of nonequilibrium thermodynamics, and shows how the phenomenological laws of nonequilibrium thermodynamics arise in the limit of small thermal fluctuations and in the Gaussian limit where means and modes of the distribution coincide. The theory of brownian motion is assumed to be a rather general and useful model of irreversible processes that are inevitably influenced by random thermal fluctuations. The unifying approach adopted allows widely applicable principles to be extracted from the analysis of particular models, an approach which is unique to this book. The content is arranged by argument rather than by chronology. It is based on the premise that random thermal fluctuations play a decisive role in governing the evolution of nonequilibrium thermodynamic processes. Also that they can be viewed as a dynamic superposition of a large number of random events with the important proviso that the future evolution depends only on the present, independent of its entire past history. The book is intended for nonmathematicians working in the areas of nonequilibrium thermodynamics and statistical mechanics. Those interested will include chemical physicists working on nonlinear dynamic phenomena, solid state physics and those working in the field of nonlinear optics. Because of the interdisciplinary nature of nonequilibrium thermodynamics research, theoretical biologists, economists and engineers will find this book of value. Contents Preface Nonequilibrium Thermodynamics Brownian Motion Theory Stochastic Foundations of Nonequilibrium Thermodynamics Onsager-Machlup Theory The Kinetic Analog of Boltzmann's Principle Stochastic H Theorem The Thermodynamic Limit Index
