Particle transport in a correlated ratchet

TL;DR

This paper investigates how correlated noise influences particle transport in a ratchet system, revealing counterintuitive effects on current magnitude and displacement, with implications for biological matter.

Contribution

It introduces a detailed analysis of particle dynamics in a tilted colored noise ratchet, highlighting novel effects of noise correlation and resetting on current and displacement.

Findings

Current decreases with increasing noise correlation when noise is reset at transitions.

Current increases with noise correlation when noise evolves freely.

Optimal noise strength maximizes current in the free-evolving noise scenario.

Abstract

One of the many measures of the non-equilibrium nature of a system is the existence of a non-zero steady state current which is especially relevant for many biological systems. To this end, we study the non-equilibrium dynamics of a particle moving in a tilted colored noise ratchet in two different situations. In the first, the colored noise variable is reset to a specific value every time the particle transitions from one well to another in the ratchet. Contrary to intuition, we find that the current magnitude decreases as the correlation time of the noise increases, and increases monotonically with noise strength. The average displacement of the particle is against the tilt, which implies that the particle performs work. We then consider a variation of the same problem in which the colored noise process is allowed to evolve freely without any resetting at the transitions. Again, the average displacement is against the potential. However, the current magnitude increases with the correlation time, and there is an optimal noise strength that maximizes the current magnitude. Finally, we provide quantitative arguments to explain these findings and their relevance to active biological matter such as tissues.