Monotonic Return to Steady Nonequilibrium

Christian Maes, Karel Netočný, and Bram Wynants
Phys. Rev. Lett. 107, 010601 – Published 29 June 2011

Abstract

We propose and analyze a new candidate Lyapunov function for relaxation towards general nonequilibrium steady states. The proposed functional is obtained from the large time asymptotics of time-symmetric fluctuations. For driven Markov jump or diffusion processes it measures an excess in dynamical activity rates. We present numerical evidence and we report on a rigorous argument for its monotonic time dependence close to the steady nonequilibrium or in general after a long enough time. This is in contrast with the behavior of approximate Lyapunov functions based on entropy production that when driven far from equilibrium often keep exhibiting temporal oscillations even close to stationarity.

  • Figure
  • Received 15 February 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.010601

© 2011 American Physical Society

Authors & Affiliations

Christian Maes

  • Instituut voor Theoretische Fysica, K. U. Leuven, 3001 Leuven, Belgium

Karel Netočný

  • Institute of Physics AS CR, Praha 8, CZ - 182 21, Czech Republic

Bram Wynants

  • Institut de Physique Théorique, CEA-Saclay, F-91191 Gif-sur-Yvette Cedex, France

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Issue

Vol. 107, Iss. 1 — 1 July 2011

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