Optimal estimates of free energies from multi-state nonequilibrium work data

TL;DR

This paper introduces an optimal maximum likelihood method to estimate free energies from nonequilibrium work data across multiple thermodynamic states, enhancing efficiency in simulations and experiments.

Contribution

It develops a new maximum likelihood approach that reweights all pathways for free energy estimation from nonequilibrium data, applicable to both simulations and experiments.

Findings

Significant efficiency improvements when combined with parallel tempering.

Effective estimation of free energies from forward and reverse work measurements.

Applicable to alchemical mutations of amino acids.

Abstract

We derive the optimal estimates of the free energies of an arbitrary number of thermodynamic states from nonequilibrium work measurements; the work data are collected from forward and reverse switching processes and obey a fluctuation theorem. The maximum likelihood formulation properly reweights all pathways contributing to a free energy difference, and is directly applicable to simulations and experiments. We demonstrate dramatic gains in efficiency by combining the analysis with parallel tempering simulations for alchemical mutations of model amino acids.