Number of trials required to estimate a free-energy difference, using fluctuation relations

TL;DR

This paper develops a new theoretical framework to estimate the number of trials needed for accurate free-energy difference calculations using fluctuation relations, incorporating information theory and bidirectionality to improve bounds.

Contribution

It introduces an information-theoretic bound on the number of trials for free-energy estimation, enhancing previous rough estimates with a rigorous approach that accounts for atypical trials.

Findings

Bound on trial number using order-infinity Renyi entropy

Improved estimates with bidirectionality practice

Numerical validation on classical gas simulations

Abstract

The difference Delta F between free energies has applications in biology, chemistry, and pharmacology. The value of Delta F can be estimated from experiments or simulations, via fluctuation theorems developed in statistical mechanics. Calculating the error in a Delta F estimate is difficult. Worse, atypical trials dominate estimates. How many trials one should perform was estimated roughly in [Jarzynski, Phys. Rev. E 73, 046105 (2006)]. We enhance the approximation with information-theoretic strategies: We quantify "dominance" with a tolerance parameter chosen by the experimenter or simulator. We bound the number of trials one should expect to perform, using the order-infinity Renyi entropy. The bound can be estimated if one implements the "good practice" of bidirectionality, known to improve estimates of Delta F. Estimating Delta F from this number of trials leads to an error that we bound approximately. Numerical experiments on a weakly interacting dilute classical gas support our analytical calculations.