Equilibrium free energy differences from a linear nonequilibrium equality

TL;DR

This paper introduces a linear nonequilibrium equality method, using variational shortcuts to isothermality, that efficiently estimates free energy differences with faster convergence than traditional nonlinear methods, especially in fast, dissipative processes.

Contribution

The paper presents a novel linear nonequilibrium equality approach utilizing variational shortcuts to isothermality for more accurate free energy estimation.

Findings

Method achieves high accuracy in free energy estimation.

Outperforms nonlinear equality in fast, dissipative processes.

Validated through simulations of a Brownian particle in a double-well potential.

Abstract

Extracting equilibrium information from nonequilibrium measurements is a challenge task of great importance in understanding the thermodynamic properties of physical, chemical, and biological systems. The discovery of the Jarzynski equality illumines the way to estimate the equilibrium free energy difference from the work performed in nonequilibrium driving processes. However, the nonlinear (exponential) relation causes the poor convergence of the Jarzynski equality. Here, we propose a concise method to estimate the free energy difference through a linear nonequilibrium equality which inherently converges faster than nonlinear nonequilibrium equalities. This linear nonequilibrium equality relies on an accelerated isothermal process which is realized by using a unified variational approach, named variational shortcuts to isothermality. We apply our method to an underdamped Brownian particle moving in a double-well potential. The simulations confirm that the method can be used to accurately estimate the free energy difference with high efficiency. Especially during fast driving processes with high dissipation, the method can improve the accuracy by more than an order of magnitude compared with the estimator based on the nonlinear nonequilibrium equality.