Calculating the free energy difference by applying the Jarzynski equality to a virtual integrable system

TL;DR

This paper introduces a novel method using an integrable virtual system with the Jarzynski equality to compute free energy differences more efficiently by transforming a nonequilibrium problem into an equilibrium one.

Contribution

It proposes a new approach that simplifies free energy calculations by employing an integrable virtual system, reducing computational costs significantly.

Findings

Efficient free energy calculation via virtual integrable systems.

Reduction in computational cost compared to traditional methods.

Validated with numerical studies on model systems.

Abstract

The Jarzynski equality (JE) provides a nonequilibrium method to measure and calculate the free energy difference (FED). Note that if two systems share the same Hamiltonian at two equilibrium states, respectively, they share the same FED between these two equilibrium states as well. Therefore the calculation of the FED of a system may be facilitated by considering instead another virtual system designed to this end. Taking advantage of this flexibility and the JE, we show that by introducing an integrable virtual system, the evolution problem involved in the JE can be solved. As a consequence, FED is expressed in the form of an equilibrium equality, in contrast with the nonequilibrium JE it is based on. Numerically, this result allows FED to be computed by sampling the canonical ensemble directly and the computational cost can be significantly reduced. The effectiveness and efficiency of this scheme are illustrated with numerical studies of several representative model systems.