The modified Sutherland--Einstein relation for diffusive nonequilibria

TL;DR

This paper explores how the classical relation between diffusion and mobility is modified in nonequilibrium conditions, providing theoretical insights and simulations to illustrate the correction terms and their dependencies.

Contribution

It introduces a modified fluctuation-dissipation relation for nonequilibrium Langevin systems, including explicit correction terms and a decomposition of the mobility matrix.

Findings

Diffusion depends more strongly on external forcing than mobility.

The mobility matrix deviates from proportionality to diffusion in nonequilibrium.

Explicit decomposition of the symmetrized mobility matrix into positive matrices.

Abstract

There remains a useful relation between diffusion and mobility for a Langevin particle in a periodic medium subject to nonconservative forces. The usual fluctuation-dissipation relation easily gets modified and the mobility matrix is no longer proportional to the diffusion matrix, with a correction term depending explicitly on the (nonequilibrium) forces. We discuss this correction by considering various simple examples and we visualize the various dependencies on the applied forcing and on the time by means of simulations. For example, in all cases the diffusion depends on the external forcing more strongly than does the mobility. We also give an explicit decomposition of the symmetrized mobility matrix as the difference between two positive matrices, one involving the diffusion matrix, the other force--force correlations.