Work fluctuations for diffusion dynamics submitted to stochastic return

Returning a system to a desired state under a force field involves a thermodynamic cost, i.e. 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 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.

Automated summary

This article introduces a general framework for determining the work distribution for returning a system using a confining potential with its minimum at the restart location. The average over resetting pathways provides a robust method for accessing statistical information of observables from resetting systems. The theory is illustrated using specific computations and validated through numerical simulations, revealing non-trivial behaviors of work fluctuations.