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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
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.
Bibliographic Information
Book Title: Mathematical Theory of Nonequilibrium Steady States
Book Subtitle: On the Frontier of Probability and Dynamical Systems
Authors: Da-Quan Jiang, Min Qian, Min-Ping Qian
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b94615
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2004
Softcover ISBN: 978-3-540-20611-8Published: 08 December 2003
eBook ISBN: 978-3-540-40957-1Published: 09 December 2003
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 286
Topics: Probability Theory and Stochastic Processes, Dynamical Systems and Ergodic Theory, Global Analysis and Analysis on Manifolds, Complex Systems, Statistical Physics and Dynamical Systems