Large deviations of the empirical current in interacting particle systems

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.

26 pages

References in corpus (3)

• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Macroscopic current fluctuations in stochastic lattice gases
• Large deviations for a stochastic model of heat flow

Cited by in corpus (11)

• Stochastic interacting particle systems out of equilibrium
• Large deviations conditioned on large deviations II: Fluctuating hydrodynamics
• Vortices in the two-dimensional Simple Exclusion Process
• Strong asymmetric limit of the quasi-potential of the boundary driven weakly asymmetric exclusion process
• Dynamical Phase Transitions for Flows on Finite Graphs
• Stochastic Dynamics, Large Deviations Principle, and Non-equilibrium Thermodynamics
• The moving particle lemma for the exclusion process on a weighted graph
• Minimum Dissipation Principle in Nonlinear Transport
• Full Current Statistics for a Disordered Open Exclusion Process
• Hydrodynamic limit of an exclusion process with vorticity
• Nonequilibrium Response from the dissipative Liouville Equation