04955nam 22008535 450 991014461990332120200701230226.03-540-40957-210.1007/b94615(CKB)1000000000230915(SSID)ssj0000324699(PQKBManifestationID)11251062(PQKBTitleCode)TC0000324699(PQKBWorkID)10332243(PQKB)10749103(DE-He213)978-3-540-40957-1(MiAaPQ)EBC6283824(MiAaPQ)EBC5592001(Au-PeEL)EBL5592001(OCoLC)1066184930(PPN)238049051(EXLCZ)99100000000023091520121227d2004 u| 0engurnn|008mamaatxtccrMathematical Theory of Nonequilibrium Steady States On the Frontier of Probability and Dynamical Systems /by Da-Quan Jiang, Min Qian, Ming-Ping Qian1st ed. 2004.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2004.1 online resource (X, 286 p.) Lecture Notes in Mathematics,0075-8434 ;1833Bibliographic Level Mode of Issuance: Monograph3-540-20611-6 Includes bibliographical references (pages [253]-276) and index.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.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.Lecture Notes in Mathematics,0075-8434 ;1833ProbabilitiesDynamicsErgodic theoryGlobal analysis (Mathematics)Manifolds (Mathematics)Statistical physicsDynamicsProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XGlobal Analysis and Analysis on Manifoldshttps://scigraph.springernature.com/ontologies/product-market-codes/M12082Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Probabilities.Dynamics.Ergodic theory.Global analysis (Mathematics)Manifolds (Mathematics)Statistical physics.Dynamics.Probability Theory and Stochastic Processes.Dynamical Systems and Ergodic Theory.Global Analysis and Analysis on Manifolds.Complex Systems.Statistical Physics and Dynamical Systems.530Jiang Da-Quanauthttp://id.loc.gov/vocabulary/relators/aut282247Qian Minauthttp://id.loc.gov/vocabulary/relators/autQian Ming-Pingauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910144619903321Mathematical Theory of Nonequilibrium Steady States2512069UNINA