Heat flow due to time-delayed feedback
Heat flow due to time-delayed feedback
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DOI：
10.1038/s41598-019-39320-0
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发表时间：
2019-02-21
影响因子：
4.6
通讯作者：
Klapp, Sabine H. L.
中科院分区：
文献类型：
--
作者：
Loos, Sarah A. M.;Klapp, Sabine H. L.
生物学、物理学和技术中的许多随机系统在基本运动方程中涉及离散时间延迟，例如，有限的信号传输时间或信号检测与设备的适配之间的时滞。从数学的角度来看，延迟系统代表了一类特殊的非马尔可夫过程与delta-peaked内存内核。众所周知，延迟可以引起有趣的行为，如自发振荡，或由延迟和噪声之间的相互作用引起的共振现象。然而，时滞随机系统的热力学仍然是广泛未开发的。这对于由非线性力控制的连续系统尤其如此，这些力在现实情况中无处不在。本文提出了一种求解时滞反馈作用下经典过阻尼系统稳态热耗率的解析方法。我们发现，反馈不可避免地导致一个有限的热流，即使是消失的小延迟时间，并检测噪声和延迟的非平凡的相互作用的根本原因。为了说明这一点，并提供一个理解的热流在小的延迟时间低于速度弛豫时间尺度，我们比较的情况下，欠阻尼运动的“熵泵”的现象已经建立。应用到一个示例性的（过阻尼）的反馈系统表明，反馈诱导加热以及冷却制度，并导致在相干共振条件下的介质熵产生的最大值。原则上，这些观察结果在涉及胶体悬浮液的实验中是可测量的。
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.