Memory effects in nonlinear transport: kinetic equations and ratchet devices

TL;DR

This paper introduces a new method to derive kinetic equations with memory effects for nonlinear transport systems, applying it to anomalous diffusion and a novel ratchet mechanism influenced by thermodynamic coupling.

Contribution

It develops a generalized Fokker-Planck equation with memory effects within mesoscopic thermodynamics, and proposes a new ratchet mechanism driven by Onsager coupling.

Findings

Analyzes non-Markovian dynamics of anomalous diffusion.

Proposes a thermodynamically coupled ratchet mechanism.

Examines fluctuation-dissipation theorem validity in non-Markovian systems.

Abstract

We present a new method to derive kinetic equations for systems undergoing non-linear transport in the presence of memory effects. In the framework of mesoscopic nonequilibrium thermodynamics, we derive a generalized Fokker-Planck equation incorporating memory effects through time-dependent coefficients. As applications, we first discuss the non-Markovian dynamics of anomalous diffusion in a potential, analyzing the validity of the fluctuation-dissipation theorem. In a second application, we propose a new ratchet mechanism in which the periodic driving acting on the particle is induced by the Onsager coupling of the diffusion current with an oscillating thermodynamic force.