Mathematical theory of nonequilibrium steady states
Subtitle: on the frontier of probability and dynamical systems
By: Da-Quan Jiang, Min Qian, Min-Ping Qian
Contributors: Qian, Min, 1927-; Qian, Min-Ping
Series: Lecture notes in mathematics -- 1833; Lecture notes in mathematics (Springer-Verlag) -- 1833.
Publisher: Springer
Published: 2004
Place of publication: Berlin; New York
Language: eng
Number of pages: 280
Subjects: Statistical thermodynamics; Nonequilibrium thermodynamics; Nonequilibrium statistical mechanics; Markov processes
Description: This volume provides a systematic mathematical exposition of the conceptual problems of nonequilibrium statistical physics, such as entropy production, irreversibility, and ordered phenomena. Markov chains, diffusion processes, and hyperbolic dynamical systems are used as mathematical models of physical systems. A measure-theoretic definition of entropy production rate and its formulae in various cases are given. It vanishes if and only if the stationary system is reversible and in equilibrium. Moreover, in the cases of Markov chains and diffusion processes on manifolds, it can be expressed in terms of circulations on directed cycles. Regarding entropy production fluctuations, the Gallavotti-Cohen fluctuation theorem is rigorously proved.
Notes: Includes bibliographical references (p. 253-276) and index.