Non-Equilibrium Currents in Stochastic Field Theories: a Geometric Insight

TL;DR

This paper introduces a geometric formalism to analyze nonequilibrium steady-state currents in stochastic field theories, enabling the prediction and observation of physical manifestations of abstract probability currents.

Contribution

It develops a novel geometric approach using an extended exterior derivative to identify local rotations and predict physical space currents in nonequilibrium systems.

Findings

Observed steady-state currents in Active Model B during phase separation.

Measured propagating modes in the KPZ equation.

Linked abstract probability currents to real-space phenomena.

Abstract

We introduce a new formalism to study nonequilibrium steady-state currents in stochastic field theories. We show that generalizing the exterior derivative to functional spaces allows identifying the subspaces in which the system undergoes local rotations. In turn, this allows predicting the counterparts in the real, physical space of these abstract probability currents. The results are presented for the case of the Active Model B undergoing motility-induced phase separation, which is known to be out of equilibrium but whose steady-state currents have not yet been observed, as well as for the KPZ equation. We locate and measure these currents and show that they manifest in real space as propagating modes localized in regions with non-vanishing gradients of the fields.