Non equilibrium current fluctuations in stochastic lattice gases

Details Non equilibrium current fluctuations in stochastic lattice gases Non equilibrium current fluctuations in stochastic lattice gases

2005-06-24

arxiv.org/abs/cond-mat/0506664v1

J. Stat. Phys. (2006) 123, 237-276

Physics

Condensed Matter

Statistical Mechanics

36 Pages, No figure

Scientific paper

10.1007/s10955-006-9056-4

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation $j$ of the empirical current with a rate functional $\mc I (j)$. We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional $\mc I $. We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of $\mc I$ and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.

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