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On the definition of entropy production, via examples. (English) Zbl 0977.82025

Summary: We present a definition of entropy production rate for classes of deterministic and stochastic dynamics. The point of departure is a Gibbsian representation of the steady state path space measure for which “the density” is determined with respect to the time-reversed process. The Gibbs formalism is used as a unifying algorithm capable of incorporating basic properties of entropy production in nonequilibrium systems. Our definition is motivated by recent work on the Gallavotti-Cohen (local) fluctuation theorem and it is illustrated via a number of examples [see also C. Maes, J. Stat. Phys. 95, 367-392 (1999; Zbl 0941.60099) and and J. L. Lebowitz and H. Spohn, ibid. 95, 333-365 (1999; Zbl 0934.60090)].

MSC:

82C03 Foundations of time-dependent statistical mechanics
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
82C22 Interacting particle systems in time-dependent statistical mechanics
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