Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes

TL;DR

This paper investigates the entropy production and time reversal in time-inhomogeneous diffusion processes, revealing connections to optimal control and importance sampling, with implications for nonequilibrium statistical mechanics.

Contribution

It introduces new bounds on entropy production and links the time reversal of reverse processes to optimal control in diffusion processes.

Findings

Derived upper bounds on relative entropy production.

Established that time reversal of the reverse process matches the optimal control process.

Connected the reverse process to zero-variance importance sampling in Jarzynski's equality.

Abstract

This paper studies time-inhomogeneous nonequilibrium diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy production of the time-inhomogeneous process with respect to the transient invariant probability measures. We also study the time reversal of the reverse process in Crooks' fluctuation theorem. We show that the time reversal of the reverse process coincides with the optimally controlled forward process that leads to zero variance importance sampling estimator based on Jarzynski's equality.