The European Physical Journal Special Topics

, Volume 224, Issue 5, pp 905–925 | Cite as

Time reversal invariance, entropy production and work dissipation in stochastic thermodynamics

  • B. Gaveau
  • M. Moreau
Regular Article
Part of the following topical collections:
  1. Discussion and Debate: The Carnot Principle Revisited: Towards New Extensions?


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.


European Physical Journal Special Topic Power Dissipation Entropy Production Detailed Balance Time Reversal Invariance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  • B. Gaveau
    • 1
  • M. Moreau
    • 1
  1. 1.University Pierre et Marie Curie, LPTMC, case 121Paris Cedex 05France

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