Near-equilibrium measurements of nonequilibrium free energy

TL;DR

This paper derives a new method to measure the free energy of non-equilibrium systems using path ensemble averages, providing a practical approximation that is accurate near equilibrium.

Contribution

It introduces a formally exact expression for non-equilibrium free energy and a simple near-equilibrium approximation based on measurable work, advancing experimental thermodynamics.

Findings

The approximation accurately estimates free energy in simple models.

The method involves path ensemble averages of work over time-reversed trajectories.

The approach is experimentally feasible for real systems.

Abstract

A central endeavor of thermodynamics is the measurement of free energy changes. Regrettably, although we can measure the free energy of a system in thermodynamic equilibrium, typically all we can say about the free energy of a non-equilibrium ensemble is that it is larger than that of the same system at equilibrium. Herein, we derive a formally exact expression for the probability distribution of a driven system, which involves path ensemble averages of the work over trajectories of the time-reversed system. From this we find a simple near-equilibrium approximation for the free energy in terms of an excess mean time-reversed work, which can be experimentally measured on real systems. With analysis and computer simulation, we demonstrate the accuracy of our approximations for several simple models.