Large deviations in weakly interacting boundary driven lattice gases

TL;DR

This paper investigates large deviations and correlation structures in weakly interacting boundary-driven lattice gases, revealing how boundary drive influences correlations and supports an additivity principle.

Contribution

It provides first-order calculations of density profiles, correlations, and large deviation functions for both zero-range and short-range lattice gases under boundary drive.

Findings

Boundary drive induces long-range correlations only in short-range dynamics.

The large deviation function supports the additivity principle.

Explicit first-order expressions for density and current distributions.

Abstract

One-dimensional, boundary-driven lattice gases with local interactions are studied in the weakly interacting limit. The density profiles and the correlation functions are calculated to first order in the interaction strength for zero-range and short-range processes differing only in the specifics of the detailed-balance dynamics. Furthermore, the effective free-energy (large-deviation function) and the integrated current distribution are also found to this order. From the former, we find that the boundary drive generates long-range correlations only for the short-range dynamics while the latter provides support to an additivity principle recently proposed by Bodineau and Derrida.