Computing diffusivities from particle models out of equilibrium

TL;DR

This paper introduces a novel numerical method to determine diffusivity from stochastic particle systems out of equilibrium, applicable to experimental data, by leveraging the fluctuation-dissipation relation in large particle systems.

Contribution

The paper presents a new approach to extract diffusivities from particle models out of equilibrium, extending applicability to experimental data and complex nonlinear systems.

Findings

Successfully applied to three classic particle models.

Allows comparison with analytical solutions.

Works under out of equilibrium conditions with Gaussian fluctuations.

Abstract

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but is otherwise allowed to undergo arbitrary out of equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation-dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions.