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Time-reversed dynamical entropy and irreversibility in Markovian random processes. (English) Zbl 1113.82036

J. Stat. Phys. 117, No. 3-4, 599-615 (2004); erratum ibid. 126, No. 4-5, 1109 (2007).
Summary: A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states.

MSC:

82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
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