Mathematical theory of nonequilibrium steady states : on the frontier of probability and dynamical systems
Thisvolume 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. TOC: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.
- Standort
-
Deutsche Nationalbibliothek Frankfurt am Main
- ISBN
-
9783540206118
3540206116
- Maße
-
24 cm
- Umfang
-
IX, 280 S.
- Sprache
-
Englisch
- Anmerkungen
-
Literaturverz. S. 253 - 276
- Erschienen in
-
Lecture notes in mathematics ; 1833
- Klassifikation
-
Physik
- Schlagwort
-
Nichtgleichgewichtsstatistik
Stochastischer Prozess
Dynamisches System
- Ereignis
-
Veröffentlichung
- (wo)
-
Berlin, Heidelberg, New York, Hong Kong, London, Milan, Paris, Tokyo
- (wer)
-
Springer
- (wann)
-
2004
- Urheber
- Inhaltsverzeichnis
- Rechteinformation
-
Bei diesem Objekt liegt nur das Inhaltsverzeichnis digital vor. Der Zugriff darauf ist unbeschränkt möglich.
- Letzte Aktualisierung
-
11.06.2025, 13:35 MESZ
Datenpartner
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
- Jiang, Da-Quan
- Qian, Min
- Qian, Min-Ping
- Springer
Entstanden
- 2004
Ähnliche Objekte (12)
Nonequilibrium dynamical mean-field theory
Understanding non-equilibrium thermodynamics : foundations, applications, frontiers
Nonequilibrium steady-state physics with quantum master equations
Nonequilibrium steady-state transport in quantum impurity models
Emergent second law for non-equilibrium steady states
Non-Equilibrium Steady States for Chains of Four Rotors
Non-equilibrium steady state formation in 3+1 dimensions
Non-equilibrium steady state formation in 3+1 dimensions
Nonequilibrium steady state in a periodically driven Kondo model
Non-equilibrium steady state formation in 3+1 dimensions
Nonequilibrium density-matrix description of steady-state quantum transport
Learning nonequilibrium statistical mechanics and dynamical phase transitions
Nonequilibrium dynamical mean-field theory
Understanding non-equilibrium thermodynamics : foundations, applications, frontiers
Nonequilibrium steady-state physics with quantum master equations
Nonequilibrium steady-state transport in quantum impurity models
Emergent second law for non-equilibrium steady states
Non-Equilibrium Steady States for Chains of Four Rotors
Non-equilibrium steady state formation in 3+1 dimensions
Non-equilibrium steady state formation in 3+1 dimensions
Nonequilibrium steady state in a periodically driven Kondo model
Non-equilibrium steady state formation in 3+1 dimensions
Nonequilibrium density-matrix description of steady-state quantum transport
Learning nonequilibrium statistical mechanics and dynamical phase transitions
Nonequilibrium dynamical mean-field theory
Understanding non-equilibrium thermodynamics : foundations, applications, frontiers
Nonequilibrium steady-state physics with quantum master equations
Nonequilibrium steady-state transport in quantum impurity models
Emergent second law for non-equilibrium steady states
Non-Equilibrium Steady States for Chains of Four Rotors
Non-equilibrium steady state formation in 3+1 dimensions
Non-equilibrium steady state formation in 3+1 dimensions
Nonequilibrium steady state in a periodically driven Kondo model
Non-equilibrium steady state formation in 3+1 dimensions
Nonequilibrium density-matrix description of steady-state quantum transport