Eulerian and Lagrangian pictures of non-equilibrium diffusions

TL;DR

This paper demonstrates that non-equilibrium diffusions can be viewed as equilibrium systems in a Lagrangian frame, explaining the observed fluctuation-dissipation relations and providing insights into stochastic particle dynamics.

Contribution

It introduces a Lagrangian perspective showing non-equilibrium diffusions exhibit equilibrium properties in their mean local velocity frame, a novel conceptual approach.

Findings

Non-equilibrium diffusions have equilibrium form in the Lagrangian frame.

Fluctuation-dissipation relations are explained by this frame perspective.

Illustrated with examples of stochastic particle dynamics.

Abstract

We show that a non-equilibrium diffusive dynamics in a finite-dimensional space takes in the Lagrangian frame of its mean local velocity an equilibrium form with the detailed balance property. This explains the equilibrium nature of the fluctuation-dissipation relations in that frame observed previously. The general considerations are illustrated on few examples of stochastic particle dynamics.