Journal of Statistical Physics

, Volume 117, Issue 3, pp 599–615

Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes

  • Pierre Gaspard

DOI: 10.1007/s10955-004-3455-1

Cite this article as:
Gaspard, P. Journal of Statistical Physics (2004) 117: 599. doi:10.1007/s10955-004-3455-1


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.

Dynamical randomness entropy per unit time Kolmogorov Sinai entropy entropy production time reversal nonequilibrium steady state stochastic process Markov chain jump process chemical reaction 

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • Pierre Gaspard
    • 1
  1. 1.Center for Nonlinear Phenomena and Complex SystemsUniversité Libre de BruxellesBrusselsBelgium