Time reversal invariance, entropy production and work dissipation in stochastic thermodynamics
University Pierre et Marie Curie, LPTMC, case 121, 4 place Jussieu, 75252 Paris Cedex 05, France
Received: 16 December 2014
Revised: 7 May 2015
Published online: 17 July 2015
We consider the work production in a mesosccopic Markov system obeying discrete stochastic dynamics with time-dependent constraints. Using asymmetry relations presented elsewhere, which result from time reversal invariance of the underlying microscopic system, we derive, beside known equalities in stochastic thermodynamics, a new result: the “Carnot equality”, that generalizes the Carnot relation for macroscopic bi-thermal engines. Such equalities, which extend the classical inequalities of thermodynamics, result from microscopic time reversal invariance only. On the other hand we show that, on the mesoscopic level, notions such as entropy production and power dissipation per transition cannot always be defined. In the absence of a precise mechanical model, such definitions are possible if, and only if, the asymmetry relations due to microscopic time reversal invariance are supplemented by space symmetry relations, equivalent to parity, which are not always satisfied. This article is supplemented with comments by J.M.R. Parrondo and L. Granger and a final reply by the authors.
© EDP Sciences, Springer-Verlag, 2015