© 2004

Mathematical Theory of Nonequilibrium Steady States

On the Frontier of Probability and Dynamical Systems

  • Authors

Part of the Lecture Notes in Mathematics book series (LNM, volume 1833)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Da-Quan Jiang, Min Qian, Min-Ping Qian
    Pages 1-10
  3. Da-Quan Jiang, Min Qian, Min-Ping Qian
    Pages 149-158
  4. Da-Quan Jiang, Min Qian, Min-Ping Qian
    Pages 159-188
  5. Da-Quan Jiang, Min Qian, Min-Ping Qian
    Pages 189-214
  6. Da-Quan Jiang, Min Qian, Min-Ping Qian
    Pages 253-276
  7. Back Matter
    Pages 277-280

About this book


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.


Markov chain Markov processes diffusion process entropy production rate hyperbolic dynamical systems irreversibility nonequilibrium statistical physics statistical physics

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