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Thermodynamic large fluctuations from uniformized dynamics David Andrieux

Summary: Thermodynamic large fluctuations from uniformized dynamics
David Andrieux
Department of Neurobiology and Kavli Institute for Neuroscience, Yale University School of Medicine,
New Haven, Connecticut 06510, USA
and Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, B-1050 Brussels, Belgium
Received 13 April 2010; revised manuscript received 7 June 2010; published 20 September 2010
Large fluctuations have received considerable attention as they encode information on the fine-scale dynam-
ics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermody-
namical properties. Here we report that, using the technique of uniformization, the thermodynamic large
deviation functions of continuous-time Markov processes can be obtained from Markov chains evolving in
discrete time. This formulation offers theoretical and numerical approaches to explore large deviation proper-
ties. In particular, the time evolution of autonomous and nonautonomous processes can be expressed in terms
of a single Poisson rate. In this way the uniformization procedure leads to a simple and efficient way to
simulate stochastic trajectories that reproduce the exact fluxes statistics. We illustrate the formalism for the
current fluctuations in a stochastic pump model.
DOI: 10.1103/PhysRevE.82.031124 PACS number s : 05.40. a, 05.70.Ln
Many natural phenomena are successfully described at the
mesoscopic level in terms of Markovian random processes
1­3 . Examples of such jump processes range from birth-


Source: Andrieux, David - Service de Physique Non-Linéaire and Mécanique Statistique, Université Libre de Bruxelles


Collections: Physics; Biology and Medicine