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

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.

List of contents

Preface.- Introduction.- Circulation Distribution, Entropy Production and Irreversibility of Denumerable Markov Chains.- Circulation Distribution, Entropy Production and Irreversibility of Finite Markov Chains with Continuous Parameter.- General Minimal Diffusion Process: its Construction, Invariant Measure, Entropy Production and Irreversibility.- Measure-theoretic Discussion on Entropy Production of Diffusion Processes and Fluctuation-dissipation Theorem.- Entropy Production, Rotation Numbers and Irreversibility of Diffusion Processes on Manifolds.- On a System of Hyperstable Frequency Locking Persistence under White Noise.- Entropy Production and Information Gain in Axiom A Systems.- Lyapunov Exponents of Hyperbolic Attractors.- Entropy Production, Information Gain and Lyapunov Exponents of Random Hyperbolic Dynamical Systems.- References.- Index.

Summary

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.

Product details

• Authors: D.-Q. Jiang, Da-Qua Jiang, Da-Quan Jiang, M. Qian, M.-P. Qian, Mi Qian, Min Qian, Ming-Ping Qian
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 16.01.2004
• EAN: 9783540206118
• ISBN: 978-3-540-20611-8
• No. of pages: 286
• Weight: 446 g
• Illustrations: X, 286 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; B, Dynamics, Mathematics and Statistics, Complex systems, Theoretical, Mathematical and Computational Physics, Probability Theory and Stochastic Processes, Numerical analysis, Manifolds (Mathematics), Dynamical Systems and Ergodic Theory, Ergodic theory, Nonlinear science, Dynamical systems, Probabilities, Stochastics, Probability Theory, Global analysis (Mathematics), Global Analysis and Analysis on Manifolds, Dynamics & statics, Statistical physics, Statistical Physics and Dynamical Systems