Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 123, Issue 2, Pages 237-276Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10955-006-9056-4
Keywords
stationary non equilibrium states; stochastic lattice gases; current fluctuations; Gallavotti-Cohen symmetry
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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 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 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 I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.
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