000 | 04192nam a22005895i 4500 | ||
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001 | 978-3-540-40957-1 | ||
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007 | cr nn 008mamaa | ||
008 | 121227s2004 gw | s |||| 0|eng d | ||
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_a9783540409571 _9978-3-540-40957-1 |
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_a10.1007/b94615 _2doi |
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050 | 4 | _aQA273.A1-274.9 | |
050 | 4 | _aQA274-274.9 | |
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_aPBWL _2thema |
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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. |
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300 |
_aX, 286 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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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 |
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912 | _aZDB-2-BAE | ||
999 |
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