Ratchet-mediated resetting: Current, efficiency, and exact solution

TL;DR

This paper models a Brownian particle with ratchet-mediated resetting, deriving exact solutions for its steady-state behavior, current, and efficiency, with implications for experimental resetting protocols.

Contribution

It provides the first exact analytical expressions for the probability densities, currents, and efficiency in a ratchet-mediated resetting system.

Findings

Derived exact probability densities for phases of motion.

Identified optimal current and efficiency conditions.

Validated results through simulations.

Abstract

We model an overdamped Brownian particle that is subject to resetting facilitated by a ratchet potential on a spatially periodic domain. This asymmetric potential switches on with a constant rate, but switches off again only upon the particle's first passage to a resetting point at the minimum of the potential. Repeating this cycle sustains a non-equilibrium steady-state, as well as a directed steady-state current which can be harnessed to perform useful work. We derive exact analytic expressions for the probability densities of the free-diffusion and resetting phases, the associated currents for each phase, and an efficiency parameter that quantifies the return in current for given power input. These expressions allow us to fully characterise the system and obtain experimentally relevant results such as the optimal current and efficiency. Our results are corroborated by simulations, and have implications for experimentally viable finite-time resetting protocols.