Optimal operation of feedback flashing ratchets

TL;DR

This paper investigates optimal control strategies for feedback flashing ratchets, aiming to maximize particle flux, and derives protocols for single and infinite particle cases, highlighting unresolved challenges for intermediate numbers.

Contribution

It provides the first derivation of optimal protocols for both single and infinite particle feedback flashing ratchets, advancing understanding of their control mechanisms.

Findings

Optimal protocols for one-particle ratchets identified.

Optimal protocols for infinite-particle ratchets derived.

Unsolved problem remains for finite particle numbers.

Abstract

Feedback flashing ratchets are thermal rectifiers that use information on the state of the system to operate the switching on and off a periodic potential. We discuss different strategies for this operation with the aim of maximizing the net flux of particles in the collective version of a flashing ratchet consisting on N overdamped Brownian particles. We show the optimal protocols for the one-particle ratchet and for the collective ratchet with an infinite number of particles. Finally we comment on the unsolved problem of the optimal strategy for any other number of particles.