Strong asymmetric limit of the quasi-potential of the boundary driven weakly asymmetric exclusion process

Abstract

We consider the weakly asymmetric exclusion process on a bounded interval with particles reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers equation with Dirichlet boundary conditions. In the case in which the bulk asymmetry is in the same direction as the drift due to the boundary reservoirs, we prove that the quasi-potential can be expressed in terms of the solution to a one-dimensional boundary value problem which has been introduced by Enaud and Derrida \cite{de}. We consider the strong asymmetric limit of the quasi-potential and recover the functional derived by Derrida, Lebowitz, and Speer \cite{DLS3} for the asymmetric exclusion process.

References in corpus (9)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Macroscopic fluctuation theory for stationary non equilibrium states
• Large deviation functional of the weakly asymmetric exclusion process
• Current large deviations for Asymmetric Exclusion Processes with open boundaries
• Large deviations for the boundary driven symmetric simple exclusion process
• Large deviation approach to non equilibrium processes in stochastic lattice gases
• Large deviations of the empirical current in interacting particle systems
• Static large deviations of boundary driven exclusion processes
• Hydrodynamics and hydrostatics for a class of asymmetric particle systems with open boundaries

Cited by in corpus (11)

• Macroscopic fluctuation theory
• Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile
• Dynamical large deviations for the boundary driven weakly asymmetric exclusion process
• A quasi-potential for conservation laws with boundary conditions
• Action functional and quasi-potential for the Burgers equation in a bounded interval
• Large deviation principles for nongradient weakly asymmetric stochastic lattice gases
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• Totally asymmetric limit for models of heat conduction
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Quasi-potentials in the Nonequilibrium Stationary States or a method to get explicit solutions of Hamilton-Jacobi equations
• Microscopic and macroscopic perspectives on stationary nonequilibrium states