Threshold feedback control for a collective flashing ratchet: threshold dependence

TL;DR

This paper analyzes how threshold control affects the current in a collective flashing ratchet, deriving analytical expressions and identifying optimal thresholds for different particle numbers.

Contribution

It provides analytical expressions for threshold dependence and identifies optimal thresholds for both few and many particles in a collective flashing ratchet.

Findings

Maximum current at zero thresholds for few particles.

Nonzero optimal thresholds for many particles.

Optimal thresholds for infinite particles are effective for many and few particles.

Abstract

We study the threshold control protocol for a collective flashing ratchet. In particular, we analyze the dependence of the current on the values of the thresholds. We have found analytical expressions for the small threshold dependence both for the few and for the many particle case. For few particles the current is a decreasing function of the thresholds, thus, the maximum current is reached for zero thresholds. In contrast, for many particles the optimal thresholds have a nonzero finite value. We have numerically checked the relation that allows to obtain the optimal thresholds for an infinite number of particles from the optimal period of the periodic protocol. These optimal thresholds for an infinite number of particles give good results for many particles. In addition, they also give good results for few particles due to the smooth dependence of the current up to these threshold values.