Mathematical theory of nonequilibrium steady states : on the frontier of probability and dynamical systems / Da-Quan Jiang, Min Qian, Min-Ping Qian

This book, which involves more than five hundred references, can be thought of as a synthesis, a unified approach to various models which have been previously used in the literature to study the statistical physics of nonequilibrium and more especially, entropy production, irreversibility and ordered phenomena. The main tools of modeling are denumerable Markov chains, finite Markov chains with continuous parameter, diffusion processes and hyperbolic dynamical systems. As usual, the entropy production is described by an informational divergence of which the expression is provided in various cases and it is clearly shown that the entropy production rate of a stationary system vanishes when and only when the system is reversible and in equilibrium state. A fluctuation-dissipation theorem is stated, diffusion processes on manifolds are considered and the book concludes with a chapter which exhibits the relations which may exist between entropy production, information gain, Lyapunov exponent and random hyperbolic dynamical systems. (Zentralblatt)