[share_ebook] Mathematical Theory of Nonequilibrium Steady States: On the Frontier of Probability and Dynamical Systems


Author: Da-Quan Jiang, Min Qian, and Ming-Ping Qian

Date: 2004

ISBN: 3540206116

Pages: 290

Language: English

Publisher: Springer

Format: pdf

Category: Study

Tag: Physics


Posted on 2009-01-10, by mm101.

Description

  • Author: Da-Quan Jiang, Min Qian, and Ming-Ping Qian
  • Publisher: Springer
  • Publish Date: 2004
  • ISBN: 3540206116
  • Pages: 290
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.

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