Large Deviations of the Empirical Current in Interacting Particle Systems

Authors:
  • LBL. Bertini
    L. Bertini
  • ASA. De Sole
    A. De Sole
  • DGD. Gabrielli
    D. Gabrielli
  • GJG. Jona‐Lasinio
    G. Jona‐Lasinio
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Abstract
We study current fluctuations in lattice gases in the hydrodynamic scaling limit. More precisely, we prove a large deviation principle for the empirical current in the symmetric simple exclusion process with rate functional I. We then estimate the asymptotic probability of a fluctuation of the average current over a large time interval and show that the corresponding rate function can be obtained by solving a variational problem for the functional I. For the symmetric simple exclusion process the minimizer is time independent so that this variational problem can be reduced to a time‐independent one. On the other hand, for other models the minimizer is time dependent. This phenomenon is naturally interpreted as a dynamical phase transition.
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