ENGLISH

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

By Min Qian , Da-Quan Jiang , Min-Ping Qian (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2004
ISBN
978-3-540-20611-8, 978-3-540-40957-1
DOI
10.1007/b94615
Language
english
Format
PDF
Filesize
3 MB (2830410 bytes)
Series
Lecture Notes in Mathematics 1833
Edition
1
Pages
286\276
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Dynamical Systems and ComplexityDynamical Systems and Ergodic Theory;Global Analys

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.

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