Shortcuts to isothermality and nonequilibrium work relations

TL;DR

This paper introduces a shortcut to achieve finite-rate isothermal processes, enabling the derivation of new nonequilibrium work relations and confirming them through numerical simulations of a Brownian particle.

Contribution

It proposes a novel strategy called shortcut to isothermality (STI) for finite-rate isothermal transitions and derives three new nonequilibrium work relations.

Findings

Derived a free energy-mean work identity.

Established a generalized Jarzynski equality.

Confirmed the relations via Brownian particle simulations.

Abstract

In conventional thermodynamics, it is widely acknowledged that the realization of an isothermal process for a system requires a quasi-static controlling protocol. Here we propose and design a strategy to realize a finite-rate isothermal transition from an equilibrium state to another one with same temperature, which is named shortcut to isothermality~(STI). By using STI, we unexpectedly derive three nonequilibrium work relations, including an identity between the free energy difference and the mean work due to the potential of the original system, a generalized Jarzynski equality, and the inverse relationship between the irreversible work and the total driving time. We numerically confirm these three relations by considering the motion of a Brownian particle trapped in a harmonic potential and dragged by a time-dependent force.