A forced thermal ratchet in a memory heat bath
O. Contreras-Vergara, N. S\'anchez-Salas, I. P\'erez Castillo, and J. I. Jim\'enez-Aquino

TL;DR
This paper investigates a non-Markovian thermal ratchet model with a memory-dependent friction kernel, deriving exact probability currents and analyzing how memory effects influence particle flow under external driving forces.
Contribution
It provides an exact expression for probability current in a non-Markovian ratchet with a time-dependent force, highlighting the impact of friction memory on current enhancement.
Findings
Memory effects can enhance particle current compared to Markovian cases.
Exact probability current expressions are derived for non-Markovian dynamics.
External force amplitude and bath temperature influence the flow behavior.
Abstract
The present work studies a non-Markovian forced thermal ratchet model on an asymmetric periodic potential. The Brownian dynamics is described by a generalized Langevin equation with an Ornstein-Uhlenbeck-type friction memory kernel. We show that for the case of a time-dependent driving force, also in the form of an Ornstein-Uhlenbeck-like process, an exact expression of the probability current can be derived. We also obtain the behavior of the particle's average rate of flow as a function of the external amplitude force and of the bath temperature when the driving force behaves as a square wave modulation. All our results are compared with those obtained in the Markovian case and we find, fairly remarkably, that in some cases a friction memory kernel results in an enhancement of the current
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Taxonomy
Topicsstochastic dynamics and bifurcation · Advanced Thermodynamics and Statistical Mechanics · Nonlinear Dynamics and Pattern Formation
