Variational time reversal for free energy estimation in nonequilibrium steady states

TL;DR

This paper introduces a variational method based on a modified Kawasaki-Crooks equality to accurately estimate free energy changes in nonequilibrium steady states using stochastic thermodynamics and molecular simulations.

Contribution

It develops a novel variational approach to evaluate nonequilibrium free energy corrections, improving accuracy over perturbative methods in driven and active matter models.

Findings

Enhanced accuracy in free energy estimation in nonequilibrium systems

Effective use of stochastic control theory for thermodynamic calculations

Application to models of driven and active matter

Abstract

Studying the structure of systems in nonequilibrium steady states necessitates tools that quantify population shifts and associated deformations of equilibrium free energy landscapes under persistent currents. Within the framework of stochastic thermodynamics, we establish a variant of the Kawasaki-Crooks equality that relates nonequilibrium free energy corrections in overdamped Langevin systems to heat dissipation statistics along time-reversed relaxation trajectories computable with molecular simulation. Using stochastic control theory, we arrive at a general variational approach to evaluate the Kawasaki-Crooks equality, and use it to estimate distribution functions of order parameters in specific models of driven and active matter, attaining substantial improvement in accuracy over simple perturbative methods.