Closed-loop control strategy with improved current for a flashing ratchet

TL;DR

This paper introduces a control strategy for a Brownian motor that enhances current by switching the potential based on particle position, outperforming traditional periodic methods in certain ensemble sizes.

Contribution

It proposes a novel switching protocol that improves current in collective Brownian motors, bridging the gap between single-particle and many-particle optimal control.

Findings

The protocol achieves near-optimal current for single particles.

It outperforms periodic switching in large ensembles.

Maximizing instant velocity is optimal for one particle but not for many.

Abstract

We show how to switch on and off the ratchet potential of a collective Brownian motor, depending only on the position of the particles, in order to attain a current higher than or at least equal to that induced by any periodic flashing. Maximization of instant velocity turns out to be the optimal protocol for one particle but is nevertheless defeated by a periodic switching when a sufficiently large ensemble of particles is considered. The protocol presented in this article, although not the optimal one, yields approximately the same current as the optimal protocol for one particle and as the optimal periodic switching for an infinite number of them.