A fluctuation-response relation of many Brownian particles under non-equilibrium conditions

TL;DR

This paper investigates whether the fluctuation-response relation, originally established in equilibrium, extends to non-equilibrium driven diffusive systems of interacting Brownian particles, through numerical simulations.

Contribution

It provides numerical evidence that the fluctuation-response relation applies to non-equilibrium systems with tilted periodic potentials, extending Einstein's formula.

Findings

Fluctuation-response relation holds in non-equilibrium conditions.

Linear response coefficient relates to density fluctuations similarly as in equilibrium.

Supports extension of Einstein's formula to driven diffusive systems.

Abstract

We study many interacting Brownian particles under a tilted periodic potential. We numerically measure the linear response coefficient of the density field by applying a slowly varying potential transversal to the tilted direction. In equilibrium cases, the linear response coefficient is related to the intensity of density fluctuations in a universal manner, which is called a fluctuation-response relation. We then report numerical evidence that this relation holds even in non-equilibrium cases. This result suggests that Einstein's formula on density fluctuations can be extended to driven diffusive systems when the slowly varying potential is applied in a direction transversal to the driving force.