Projected generalized free energies for non-equilibrium states

TL;DR

This paper introduces a systematic method to approximate generalized free energy in non-equilibrium stochastic systems using macroscopic observables and quasi-equilibrium distributions, revealing geometric changes at critical relaxation points.

Contribution

It presents a novel systematic procedure for approximating generalized free energy in out-of-equilibrium systems based solely on macroscopic averages.

Findings

Geometry of the approximate free energy changes at divergence points

Method applicable to systems with diverging relaxation times

Provides insights into non-equilibrium thermodynamics

Abstract

We develop a systematic procedure to approximate generalized free energy in out of equilibrium stochastic systems. The procedure only requires knowledge of the averages of macroscopic observables and uses quasi-equilibrium distribution to this task. As an application we consider model systems in the regime of diverging relaxation times. We find that geometry of the approximate generalized free energy changes at the onset of this phenomena.