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Main Title: Heat flow due to time-delayed feedback
Author(s): Loos, Sarah A. M.
Klapp, Sabine H. L.
Type: Article
Language Code: en
Abstract: Many stochastic systems in biology, physics and technology involve discrete time delays in the underlying equations of motion, stemming, e. g., from finite signal transmission times, or a time lag between signal detection and adaption of an apparatus. From a mathematical perspective, delayed systems represent a special class of non-Markovian processes with delta-peaked memory kernels. It is well established that delays can induce intriguing behaviour, such as spontaneous oscillations, or resonance phenomena resulting from the interplay between delay and noise. However, the thermodynamics of delayed stochastic systems is still widely unexplored. This is especially true for continuous systems governed by nonlinear forces, which are omnipresent in realistic situations. We here present an analytical approach for the net steady-state heat rate in classical overdamped systems subject to time-delayed feedback. We show that the feedback inevitably leads to a finite heat flow even for vanishingly small delay times, and detect the nontrivial interplay of noise and delay as the underlying reason. To illustrate this point, and to provide an understanding of the heat flow at small delay times below the velocity-relaxation timescale, we compare with the case of underdamped motion where the phenomenon of “entropy pumping” has already been established. Application to an exemplary (overdamped) bistable system reveals that the feedback induces heating as well as cooling regimes and leads to a maximum of the medium entropy production at coherence resonance conditions. These observations are, in principle, measurable in experiments involving colloidal suspensions.
Issue Date: 21-Feb-2019
Date Available: 4-Mar-2019
DDC Class: 500 Naturwissenschaften und Mathematik
600 Technik, Technologie
Subject(s): heat flow
time delays
Sponsor/Funder: DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berlin
DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzepte
Journal Title: Scientific Reports
Publisher: Nature Publishing Group
Publisher Place: London
Volume: 9
Article Number: 2491
Publisher DOI: 10.1038/s41598-019-39320-0
EISSN: 2045-2322
Appears in Collections:FG Computersimulationen und Theorie komplexer Fluide » Publications

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