Work fluctuations and Jarzynski equality in stochastic resetting

TL;DR

This paper studies work fluctuations in a stochastic resetting system with an overdamped Brownian particle, revealing universal Gaussian work distribution asymptotically and conditions under which the Jarzynski equality holds or fails.

Contribution

It introduces a theoretical framework for understanding work fluctuations under stochastic resetting and identifies protocols where the Jarzynski equality is valid or violated.

Findings

Work distribution converges to a Gaussian form at long times.

Jarzynski equality generally fails at finite times with resetting.

The equality always holds without resetting for evolving protocols.

Abstract

We consider the paradigm of an overdamped Brownian particle in a potential well, which is modulated through an external protocol, in the presence of stochastic resetting. Thus, in addition to the short range diffusive motion, the particle also experiences intermittent long jumps which reset the particle back at a preferred location. Due to the modulation of the trap, work is done on the system and we investigate the statistical properties of the work fluctuations. We find that the distribution function of the work typically, in asymptotic times, converges to a universal Gaussian form for any protocol as long as that is also renewed after each resetting event. When observed for a finite time, we show that the system does not generically obey the Jarzynski equality which connects the finite time work fluctuations to the difference in free energy, albeit a restricted set of protocols which we identify herein. In stark contrast, the Jarzynski equality is always fulfilled when the protocols continue to evolve without being reset. We present a set of exactly solvable models, demonstrate the validation of our theory and carry out numerical simulations to illustrate these findings. Finally, we have pointed out possible realistic implementations for resetting in experiments using the so-called engineered swift equilibration.