Delay-induced transport in a rocking ratchet under feedback control

Abstract

Based on the Fokker-Planck equation we investigate the transport of an overdamped colloidal particle in a static, asymmetric periodic potential supplemented by a time-dependent, delayed feedback force, $F_{\mathrm{fc}}$. For a given time $t$, $F_{\mathrm{fc}}$ depends on the status of the system at a previous time $t-{\tau }_{\mathrm{D}}$, with ${\tau }_{\mathrm{D}}$ being a delay time, specifically on the delayed mean particle displacement (relative to some "switching position"). For non-zero delay times $F_{\mathrm{fc}}(t)$ develops nearly regular oscillations generating a net current in the system. Depending on the switching position, this current is nearly as large or even larger than that in a conventional open-loop rocking ratchet. We also investigate thermodynamic properties of the delayed non-equilibrium system and we suggest an underlying Langevin equation which reproduces the Fokker-Planck results.

11 pages, 12 figures

References in corpus (11)

• Artificial Brownian motors: Controlling transport on the nanoscale
• Work and information processing in a solvable model of Maxwell's demon
• Thermodynamics of a physical model implementing a Maxwell demon
• Feedback control in a collective flashing ratchet
• Realization of a feedback controlled flashing ratchet
• Stochastic thermodynamics for "Maxwell demon" feedbacks
• Time-Delayed Feedback control of a flashing ratchet
• Effect of time delay on feedback control of a flashing ratchet
• Instabilities of localized structures in dissipative systems with delayed feedback
• Rocking feedback controlled ratchets
• Open Problems on Information and Feedback Controlled Systems

Cited by in corpus (3)

• Stochastic thermodynamics of Langevin systems under time-delayed feedback control: I. Second-law-like inequalities
• On the waiting time distribution for continuous stochastic systems
• Resonant current in coupled inertial Brownian particles with delayed-feedback control