Noise-induced rectification in out-of-equilibrium structures

TL;DR

This paper investigates how non-equilibrium random polymer structures can induce a net particle flux in overdamped systems under periodic forcing, highlighting the role of irreversibility in rectification phenomena.

Contribution

It demonstrates that out-of-equilibrium polymer structures can produce a ratchet effect even with symmetric potentials, linking irreversibility to directed motion.

Findings

Net particle flux occurs in non-equilibrium structures with symmetric potentials.

Reversal of current and non-monotonic diffusion are observed outside the adiabatic limit.

Theoretical predictions are confirmed by Langevin dynamics simulations.

Abstract

We consider the motion of overdamped particles on random potentials subjected to a Gaussian white noise and a time-dependent periodic external forcing. The random potential is modeled as the potential resulting from the interaction of a point particle with a random polymer. The random polymer is made up, by means of some stochastic process, from a finite set of possible monomer types. The process is assumed to reach a non-equilibrium stationary state, which means that every realization of a random polymer can be considered as an out-of-equilibrium structure. We show that the net flux of particles on this random medium is non-vanishing when the potential profile on every monomer is symmetric. We prove that this ratchet-like phenomenon is a consequence of the irreversibility of the stochastic process generating the polymer. On the contrary, when the process generating the polymer is at equilibrium (thus fulfilling the detailed balance condition) the system is unable to rectify the motion. We calculate the net flux of the particles in the adiabatic limit for a simple model and we test our theoretical predictions by means of Langevin dynamics simulations. We also show that, out of the adiabatic limit, the system also exhibits current reversals as well as non-monotonic dependence of the diffusion coefficient as a function of forcing amplitude.