Density-Dependent Analysis of Nonequilibrium Paths Improves Free Energy Estimates

TL;DR

This paper introduces a density-dependent analysis method for nonequilibrium paths that minimizes lag to improve the accuracy and precision of free energy difference estimates in thermodynamic systems.

Contribution

It proposes a novel analysis protocol that reduces dissipation by minimizing lag, enhancing free energy estimation from nonequilibrium paths.

Findings

Significant improvements in free energy estimate accuracy.

Reduced dissipation in trajectory reprocessing.

Effective protocols based on soluble propagators or relative entropies.

Abstract

When a system is driven out of equilibrium by a time-dependent protocol that modifies the Hamiltonian, it follows a nonequilibrium path. Samples of these paths can be used in nonequilibrium work theorems to estimate equilibrium quantities, such as free energy differences. Here, we consider analyzing paths generated with one protocol using another one. It is posited that analysis protocols which minimize the lag, the difference between the nonequilibrium and the instantaneous equilibrium densities, will reduce the dissipation of reprocessed trajectories and lead to better free energy estimates. Indeed, when minimal lag analysis protocols based on exactly soluble propagators or relative entropies are applied to several test cases, substantial gains in the accuracy and precision of estimated free energy differences are observed.