Work fluctuations for diffusion dynamics submitted to stochastic return

TL;DR

This paper develops a framework to analyze work fluctuations in diffusion systems under stochastic return protocols, revealing how to optimize return rates to minimize work fluctuation variability.

Contribution

It introduces a general method to compute work distribution in resetting systems, applicable to various setups, and explores optimization of work fluctuations through return rate tuning.

Findings

Work fluctuations can be explicitly computed for certain paradigmatic systems.

Numerical simulations confirm the theoretical predictions.

Optimizing return rate reduces work fluctuation variability.

Abstract

Returning a system to a desired state under a force field involves a thermodynamic cost, i.e., {\it work}. This cost fluctuates for a small-scale system from one experimental realization to another. We introduce a general framework to determine the work distribution for returning a system facilitated by a confining potential with its minimum at the restart location. The general strategy, based on average over {\it resetting pathways}, constitutes a robust method to gain access to the statistical information of observables from resetting systems. We exploit paradigmatic setups, where explicit computations are attainable, to illustrate the theory. Numerical simulations validate our theoretical predictions. For some of these examples, a non-trivial behavior of the work fluctuations opens a door to optimization problems. Specifically, work fluctuations can be minimized by an appropriate tuning of the return rate.