Quantifying errors in the Jarzynski estimator.

Abstract

Free energy is a crucial physical quantity in a wide range of domains, including systems at the nanoscale. The Jarzynski equality computes the equilibrium free energy difference between two states using the measurements of nonequilibrium work needed to move the system between the states. The Jarzynski equality uses the mean of the exponentiated work and thus holds true only in the limit of infinite data size. There are only a few studies estimating errors when employing the Jarzynski equality with a finite number of measurements; further, these estimates remain limited in scope. We provide nonrestrictive and rigorous confidence bounds on the free energy difference computable from samples of measured work without the need for any prior information on the work distribution. These bounds are applicable to a large variety of experimental conditions that take a system far from the equilibrium. The analytical claims are corroborated using simulations and experiments utilizing a toolbox developed in Python.