Density-Dependent Analysis of Nonequilibrium Paths Improves Free Energy Estimates II. A Feynman-Kac Formalism

TL;DR

This paper introduces a Feynman-Kac based formalism for analyzing nonequilibrium paths, which improves free energy estimates by reducing bias and variance compared to existing methods.

Contribution

It presents a novel Feynman-Kac formalism for protocol postprocessing that enhances the accuracy of free energy calculations from nonequilibrium trajectories.

Findings

Reduced bias in free energy estimates compared to Jarzynski's equality.

Demonstrated effectiveness on low-dimensional model systems.

Improved variance reduction over previous protocol analysis methods.

Abstract

The nonequilibrium fluctuation theorems have paved the way for estimating equilibrium thermodynamic properties, such as free energy differences, using trajectories from driven nonequilibrium processes. While many statistical estimators may be derived from these identities, some are more efficient than others. It has recently been suggested that trajectories sampled using a particular time-dependent protocol for perturbing the Hamiltonian may be analyzed with another one. Choosing an analysis protocol based on the nonequilibrium density was empirically demonstrated to reduce the variance and bias of free energy estimates. Here, we present an alternate mathematical formalism for protocol postprocessing based on the Feynmac-Kac theorem. The estimator that results from this formalism is demonstrated on a few low-dimensional model systems. It is found to have reduced bias compared to both the standard form of Jarzynski's equality and the previous protocol postprocessing formalism.