Using bijective maps to improve free energy estimates

TL;DR

This paper introduces a new method using bijective maps and fluctuation theorems to improve free energy difference estimates by leveraging samples from both systems' equilibrium states.

Contribution

It develops a two-sided maximum likelihood estimator based on bijective phase space mappings, enhancing free energy calculations.

Findings

Effective estimation of chemical potential in Lennard-Jones fluid

Construction and evaluation of suitable bijective maps

Improved accuracy in free energy difference estimates

Abstract

We derive a fluctuation theorem for generalized work distributions, related to bijective mappings of the phase spaces of two physical systems, and use it to derive a two-sided constraint maximum likelihood estimator of their free energy difference which uses samples from the equilibrium configurations of both systems. As an application, we evaluate the chemical potential of a dense Lennard-Jones fluid and study the construction and performance of suitable maps.