Near-equilibrium measurements of nonequilibrium free energy

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.

5 pages, 3 figures

References in corpus (7)

• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Path ensembles averages in systems driven far-from-equilibrium
• Classical and Quantum Fluctuation Theorems for Heat Exchange
• Rare events and the convergence of exponentially averaged work values
• The length of time's arrow
• An illustrative example of the relationship between dissipation and relative entropy
• Exactly solvable model illustrating far-from-equilibrium predictions

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