Nonlinear Nonequilibrium Thermodynamics I: Linear and Nonlinear Fluctuation-Dissipation Theorems

This book gives the first detailed and coherent treatment of a young and exciting branch of statistical physics. The author presents a new common theoretical framework describing both linear and nonlinear nonequilibrium thermodynamics. This first of two volumes is concerned largely with the derivation and applications of various types of fluctuation-dissipation theorems. Both theoretical physicists and applied scientists will find this material of interest since the theoretical treatment is supported by numerous illustrative examples and application of the general result to a variety of electrical, thermal, mechanical and chemical systems.

This book gives the first detailed coherent treatment of a relatively young branch of statistical physics - nonlinear nonequilibrium and fluctuation-dissipative thermo- dynamics. This area of research has taken shape fairly recently: its development began in 1959. The earlier theory -linear nonequilibrium thermodynamics - is in principle a simple special case of the new theory. Despite the fact that the title of this book includes the word "nonlinear," it also covers the results of linear nonequilibrium thermodynamics. The presentation of the linear and nonlinear theories is done within a common theoretical framework that is not subject to the linearity condition. The author hopes that the reader will perceive the intrinsic unity of this discipline, and the uniformity and generality of its constituent parts. This theory has a wide variety of applications in various domains of physics and physical chemistry, enabling one to calculate thermal fluctuations in various nonlinear systems. The book is divided into two volumes. Fluctuation-dissipation theorems (or relations) of various types (linear, quadratic and cubic, classical and quantum) are considered in the first volume. Here one encounters the Markov and non-Markov fluctuation-dissipation theorems (FDTs), theorems of the first, second and third kinds. Nonlinear FDTs are less well known than their linear counterparts.

This book gives the first detailed and coherent treatment of a young and exciting branch of statistical physics. Both theoretical physicists and applied scientists will find this material of interest since the theoretical treatment is supported by numerous illustrative examples and application of the general results to a variety of electrical, thermal, mechanical and chemical systems.