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Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes
Authors:Pierre Gaspard
Affiliation:(1) Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Brussels, Belgium
Abstract: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.
Keywords:Dynamical randomness  entropy per unit time  Kolmogorov Sinai entropy  entropy production  time reversal  nonequilibrium steady state  stochastic process  Markov chain  jump process  chemical reaction
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