A diffusive system driven by a battery or by a smoothly varying field

TL;DR

This paper analyzes the steady state of a one-dimensional diffusive system driven by a localized battery or a smooth field, revealing distinct long-range correlations from traditional reservoir-driven models despite similar density profiles.

Contribution

It introduces a model unifying battery-driven and smoothly varying field-driven diffusive systems, highlighting differences in correlation functions in the steady state.

Findings

Long-range pair correlations differ from reservoir-driven models.

Battery-driven systems exhibit unique correlation structures.

Steady state density profiles can be identical despite different correlations.

Abstract

We consider the steady state of a one dimensional diffusive system, such as the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at the origin or by a smoothly varying field along the ring. The battery appears as the limiting case of a smoothly varying field, when the field becomes a delta function at the origin. We find that in the scaling limit, the long range pair correlation functions of the system driven by a battery turn out to be very different from the ones known in the steady state of the SSEP maintained out of equilibrium by contact with two reservoirs, even when the steady state density profiles are identical in both models.