Nonequilibrium free energy estimation conditioned on measurement outcomes

TL;DR

This paper explores how measurement-based conditioning and feedback can enhance the convergence of nonequilibrium free energy estimates, building on the Jarzynski equality, and finds that discarding certain outcomes improves calculation efficiency.

Contribution

It introduces a modified Jarzynski equality incorporating measurement outcomes, demonstrating improved convergence through outcome-based discarding, linked to Bennett's acceptance ratio method.

Findings

Discarding outcomes with unwanted results improves convergence.

The modified equality relates to Bennett's acceptance ratio method.

Measurement conditioning enhances free energy estimation efficiency.

Abstract

The Jarzynski equality is one of the most influential results in the field of non equilibrium statistical mechanics. This celebrated equality allows to calculate equilibrium free energy differences from work distributions of nonequilibrium processes. In practice, such calculations often suffer from poor convergence due to the need to sample rare events. Here we examine if the inclusion of measurement and feedback can improve the convergence of nonequilibrium free energy calculations. A modified version of the Jarzynski equality in which realizations with a given outcome are kept, while others are discarded, is used. We find that discarding realizations with unwanted outcomes can result in improved convergence compared to calculations based on the Jarzynski equality. We argue that the observed improved convergence is closely related to Bennett's acceptance ratio method, which was developed without any reference to measurements or feedback.