Improving free-energy estimates from unidirectional work measurements: theory and experiment

TL;DR

This paper develops a theoretical framework and experimental validation for correcting bias in the Jarzynski free-energy estimator derived from unidirectional work measurements, applicable to various work distribution shapes.

Contribution

It introduces analytical bias expressions based on the Random Energy Model and creates an improved estimator for free-energy calculations from unidirectional data.

Findings

Accurately describes bias across different work distributions

Validates the improved estimator with DNA hairpin experiments

Demonstrates applicability to both Gaussian and non-Gaussian work data

Abstract

We derive analytical expressions for the bias of the Jarzynski free-energy estimator from N nonequilibrium work measurements, for a generic work distribution. To achieve this, we map the estimator onto the Random Energy Model in a suitable scaling limit parametrized by (log N)/m, where m measures the width of the lower tail of the work distribution, and then compute the finite-N corrections to this limit with different approaches for different regimes of (log N)/m. We show that these expressions describe accurately the bias for a wide class of work distributions, and exploit them to build an improved free-energy estimator from unidirectional work measurements. We apply the method to optical tweezers unfolding/refolding experiments on DNA hairpins of varying loop size and dissipation, displaying both near-Gaussian and non-Gaussian work distributions.