Measuring the convergence of Monte Carlo free energy calculations

TL;DR

This paper introduces a convergence measure for Bennett's acceptance ratio method in free energy calculations, helping determine if available work samples are sufficient for reliable estimates.

Contribution

It proposes a new convergence criterion for Bennett's method, enhancing the assessment of sample adequacy in free energy calculations.

Findings

The convergence measure accurately indicates sufficient sample size.

The criterion helps prevent unreliable free energy estimates.

The method is tested and shown to be statistically robust.

Abstract

The nonequilibrium work fluctuation theorem provides the way for calculations of (equilibrium) free energy based on work measurements of nonequilibrium, finite-time processes and their reversed counterparts by applying Bennett's acceptance ratio method. A nice property of this method is that each free energy estimate readily yields an estimate of the asymptotic mean square error. Assuming convergence, it is easy to specify the uncertainty of the results. However, sample sizes have often to be balanced with respect to experimental or computational limitations and the question arises whether available samples of work values are sufficiently large in order to ensure convergence. Here, we propose a convergence measure for the two-sided free energy estimator and characterize some of its properties, explain how it works, and test its statistical behavior. In total, we derive a convergence criterion for Bennett's acceptance ratio method.