Information and flux in a feedback controlled Brownian ratchet

TL;DR

This paper analyzes a feedback-controlled Brownian ratchet, demonstrating how information gathered influences flux, with an upper bound proportional to the square root of the information, bridging theoretical insights and experimental relevance.

Contribution

It provides analytic expressions for flux in feedback ratchets and establishes a quantitative relationship between information and flux performance.

Findings

Flux has an upper bound proportional to the square root of information.

Feedback ratchets outperform open-loop versions when information is utilized.

The results apply to noisy and imperfect feedback scenarios.

Abstract

We study a feedback control version of the flashing Brownian ratchet, in which the application of the flashing potential depends on the state of the particles to be controlled. Taking the view that the ratchet acts as a Maxwell's demon, we study the relationship that exists between the performance of the demon as a rectifier of random motion and the amount of information gathered by the demon through measurements. In the context of a simple measurement model, we derive analytic expressions for the flux induced by the feedback ratchet when acting on one particle and a few particles, and compare these results with those obtained with its open-loop version, which operates without information. Our main finding is that the flux in the feedback case has an upper bound proportional to the square-root of the information. Our results provide a quantitative analysis of the value of information in feedback ratchets, as well as an effective description of imperfect or noisy feedback ratchets that are relevant for experimental applications.