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3 produkter
3 produkter
Del 1833 - Lecture Notes in Mathematics
Mathematical Theory of Nonequilibrium Steady States
On the Frontier of Probability and Dynamical Systems
Häftad, Engelska, 2003
540 kr
Skickas inom 10-15 vardagar
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.
Del 1606 - Lecture Notes in Mathematics
Smooth Ergodic Theory of Random Dynamical Systems
Häftad, Engelska, 1995
593 kr
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This text studies ergodic-theoretic aspects of random dynamical systems, for example, deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems. An entropy formula of Pesin's type occupies the central part of the text whilst chapter two introduces relation numbers highlighting canonical methods in dynamical systems and measure theory. The text is intended for readers interested in noise-perturbed dynamical systems and may indicate further areas of study. Reasonable knowledge of differetial geometry, measure theory, ergodic theory, dynamical systems and preferably random processees is assumed.
Häftad, Engelska, 2009
540 kr
Skickas inom 10-15 vardagar
Smooth ergodic theory of deterministic dynamical systems deals with the study of dynamical behaviors relevant to certain invariant measures under differentiable mappingsor ows. The relevance of invariantmeasures is that they describe the f- quencies of visits for an orbit and hence they give a probabilistic description of the evolution of a dynamical system. The fact that the system is differentiable allows one to use techniques from analysis and geometry. The study of transformationsand their long-termbehavior is ubiquitousin ma- ematics and the sciences. They arise not only in applications to the real world but also to diverse mathematical disciplines, including number theory, Lie groups, - gorithms, Riemannian geometry, etc. Hence smooth ergodic theory is the meeting ground of many different ideas in pure and applied mathematics. It has witnessed a great progress since the pioneering works of Sinai, Ruelle and Bowen on Axiom A diffeomorphisms and of Pesin on non-uniformly hyperbolic systems, and now it becomes a well-developed eld.