LEADER 04955nam 22008535 450 001 9910144619903321 005 20200701230226.0 010 $a3-540-40957-2 024 7 $a10.1007/b94615 035 $a(CKB)1000000000230915 035 $a(SSID)ssj0000324699 035 $a(PQKBManifestationID)11251062 035 $a(PQKBTitleCode)TC0000324699 035 $a(PQKBWorkID)10332243 035 $a(PQKB)10749103 035 $a(DE-He213)978-3-540-40957-1 035 $a(MiAaPQ)EBC6283824 035 $a(MiAaPQ)EBC5592001 035 $a(Au-PeEL)EBL5592001 035 $a(OCoLC)1066184930 035 $a(PPN)238049051 035 $a(EXLCZ)991000000000230915 100 $a20121227d2004 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical Theory of Nonequilibrium Steady States $eOn the Frontier of Probability and Dynamical Systems /$fby Da-Quan Jiang, Min Qian, Ming-Ping Qian 205 $a1st ed. 2004. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2004. 215 $a1 online resource (X, 286 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1833 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-20611-6 320 $aIncludes bibliographical references (pages [253]-276) and index. 327 $aPreface -- 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. 330 $aThis volume provides a systematic mathematical exposition of the conceptual problems of nonequilibrium statistical physics, such as entropy production, irreversibility, and ordered phenomena. Markov chains, diffusion processes, and hyperbolic dynamical systems are used as mathematical models of physical systems. A measure-theoretic definition of entropy production rate and its formulae in various cases are given. It vanishes if and only if the stationary system is reversible and in equilibrium. Moreover, in the cases of Markov chains and diffusion processes on manifolds, it can be expressed in terms of circulations on directed cycles. Regarding entropy production fluctuations, the Gallavotti-Cohen fluctuation theorem is rigorously proved. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1833 606 $aProbabilities 606 $aDynamics 606 $aErgodic theory 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aStatistical physics 606 $aDynamics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 615 0$aProbabilities. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 0$aStatistical physics. 615 0$aDynamics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 24$aComplex Systems. 615 24$aStatistical Physics and Dynamical Systems. 676 $a530 700 $aJiang$b Da-Quan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0282247 702 $aQian$b Min$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aQian$b Ming-Ping$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144619903321 996 $aMathematical Theory of Nonequilibrium Steady States$92512069 997 $aUNINA