Molecular motor with a build-in escapement device

TL;DR

This paper investigates a classical particle in a two-component potential where random forces induce unidirectional, constant-velocity motion, resembling an escapement mechanism, with analytical and simulation results aligning well.

Contribution

It introduces a novel model of a molecular motor with an escapement-like mechanism driven by random forces, providing analytical estimates and simulation validation.

Findings

Particle exhibits unidirectional motion despite zero-mean random force.

Analytical estimates for terminal velocity match Monte Carlo simulations.

Mechanism resembles escapement devices, creating irreversibility and ballistic motion.

Abstract

We study dynamics of a classical particle in a one-dimensional potential, which is composed of two periodic components, that are time-independent, have equal amplitudes and periodicities. One of them is externally driven by a random force and thus performs a diffusive-type motion with respect to the other. We demonstrate that here, under certain conditions, the particle may move unidirectionally with a constant velocity, despite the fact that the random force averages out to zero. We show that the physical mechanism underlying such a phenomenon resembles the work of an escapement-type device in watches; upon reaching certain level, random fluctuations exercise a locking function creating the points of irreversibility in particle's trajectories such that the particle gets uncompensated displacements. Repeated (randomly) in each cycle, this process ultimately results in a random ballistic-type motion. In the overdamped limit, we work out simple analytical estimates for the particle's terminal velocity. Our analytical results are in a very good agreement with the Monte Carlo data.