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020 _a9783540409571
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024 7 _a10.1007/b94615
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
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072 7 _aMAT029000
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082 0 4 _a519.2
_223
100 1 _aJiang, Da-Quan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMathematical Theory of Nonequilibrium Steady States
_h[electronic resource] :
_bOn the Frontier of Probability and Dynamical Systems /
_cby Da-Quan Jiang, Min Qian, Min-Ping Qian.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2004.
300 _aX, 286 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1833
505 0 _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.
520 _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.
650 0 _aDistribution (Probability theory.
650 0 _aDifferentiable dynamical systems.
650 0 _aGlobal analysis.
650 0 _aStatistical physics.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
650 2 4 _aComplex Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P33000
650 2 4 _aStatistical Physics and Dynamical Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P19090
700 1 _aQian, Min.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aQian, Min-Ping.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540206118
776 0 8 _iPrinted edition:
_z9783662203699
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1833
856 4 0 _uhttps://doi.org/10.1007/b94615
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11901
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