Current Fluctuations in Stochastic Lattice Gases

Abstract

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 theory for the space-time fluctuations of the empirical current which include the previous results. We then estimate the probability of a fluctuation of the average current over a large time interval. It turns out that recent results by Bodineau and Derrida [Phys. Rev. Lett. 92, 180601 (2004)]] in certain cases underestimate this probability due to the occurrence of dynamical phase transitions.

Thermodynamic Formalism for Systems with Markov Dynamics

“…In boundary or field driven systems [8,13,38,39,40,14], for instance, this entropy flow is simply proportional to the particle current flowing through the system, the proportionality constant being the force driving the system out of equilibrium (a chemical potential or a temperature gradient, an applied field, etc.). It is characterized by a nontrivial large deviation function only for nonequilibrium systems (more precisely those breaking detailed balance but for which W (C → C ′ ) = 0 only if W (C ′ → C) = 0).…”

Vortices in the Two-Dimensional Simple Exclusion Process

“…Note that the mathematical statement from the hydrodynamic limit theory [3] relies on a more involved asymptotic with a joint space/time scaling: instead of (2.2), the large deviation function for a total current J over the microscopic time interval [0,…”

Distribution of current in nonequilibrium diffusive systems and phase transitions

“…It gives a framework to calculate a large number of properties of stochastic lattice gas, such as the large deviation functional of the density profiles. Recent developments of the hydrodynamic large deviation theory [6,7] enabled to estimate also the large deviations of the current through the system. What the MFT provide are the equations of the time evolution of the most likely density profile responsible of a given fluctuation.…”

“…Once D(ρ) and σ(ρ) are known for a given diffusive system, the probability of observing the evolution of a density profile ρ(x, s) and a rescaled current j(x, s) for 0 < s < T during a time T ∼ N 2 is given, according to the hydrodynamic large deviation theory [6], by…”