Equilibrium free energy differences at different temperatures from a single set of nonequilibrium transitions

TL;DR

This paper extends fluctuation theorems to non-equilibrium steady states, enabling the calculation of free energy differences across multiple temperatures from a single data set, thus offering a faster alternative to existing methods.

Contribution

It introduces a novel extension of Crook's Fluctuation Theorem for non-equilibrium steady states, allowing efficient computation of free energy differences at various temperatures from one transition data set.

Findings

Validated with numerical simulations using Nose-Hoover dynamics.

Able to determine free energy differences across multiple temperatures.

Faster than traditional Jarzynski and Crooks methods.

Abstract

Crook's Fluctuation Theorem and Jarzynski equality are immensely powerful tools in obtaining equilibrium properties through non-equilibrium transition between two equilibrium states. In this letter, we propose an extension to the Crook's fluctuation theorem for transition between two non-equilibrium steady states (NESS). Using the proposed theorem, we show that it is possible to obtain free energy differences of multiple equilibrium states from a single set of data obtained from the transition between two NESS. The results are verified using numerical simulations by employing Nose-Hoover dynamics and a single dimensional $\phi^4$ chain. The equations are cast in a manner that makes it possible to do experimental verification. The proposed method can provide free-energy difference for a range of temperature, and consequently is much faster than either the Jarzynski equality or the Crooks's fluctuation theorem.