Jarzynski Equality for Soret Equilibria -- Virtues of Virtual Potentials

TL;DR

This paper extends the Jarzynski equality to nonisothermal conditions, showing it applies when temperature gradients drive the system, demonstrated with colloidal particles and virtual potentials.

Contribution

It introduces a theoretical and experimental framework for applying the Jarzynski equality to nonisothermal systems using virtual potentials.

Findings

Jarzynski equality holds under nonisothermal conditions with temperature gradients.

Experimental validation with optically trapped colloidal particles.

Use of virtual potentials to measure work and heat distributions.

Abstract

The Jarzynski equality relates the free energy difference between two equilibrium states to the fluctuating irreversible work afforded to switch between them. The prescribed fixed temperature for the equilibrium states implicitly constrains the dissipative switching process that can take the system far from equilibrium. Here, we demonstrate theoretically and experimentally that such a relation also holds for the nonisothermal case, where the initial stationary state is not in equilibrium and the switching is effected by dynamically changing temperature gradients instead of a conservative force. Our demonstration employs a single colloidal particle trapped by optically induced thermophoretic drift currents. It relies on identifying suitable equivalents of classical work and heat and our ability to measure their distributions and express them in terms of a virtual potential.