Kopp Robin A, Klapp Sabine H L
Institut für Theoretische Physik, <a href="https://ror.org/03v4gjf40">Technische Universität Berlin</a>, Hardenbergstraße 36, D-10623 Berlin, Germany.
Phys Rev E. 2024 Nov;110(5-1):054126. doi: 10.1103/PhysRevE.110.054126.
Using the framework of stochastic thermodynamics we study heat production related to the stochastic motion of a particle driven by repulsive, nonlinear, time-delayed feedback. Recently it has been shown that this type of feedback can lead to persistent motion above a threshold in parameter space [R. A. Kopp et al., Phys. Rev. E 107, 024611 (2023)2470-004510.1103/PhysRevE.107.024611]. Here we investigate, numerically and by analytical methods, the rate of heat production in the different regimes around the threshold to persistent motion. We find a nonzero average heat production rate, 〈q[over ̇]〉, already below the threshold, indicating the nonequilibrium character of the system even at small feedback. In this regime, we compare to analytical results for a corresponding linearized delayed system and a small-delay approximation which provides a reasonable description of 〈q[over ̇]〉 at small repulsion (or delay time). Beyond the threshold, the rate of heat production is much larger and shows a maximum as a function of the delay time. In this regime, 〈q[over ̇]〉 can be approximated by that of a system subject to a constant force stemming from the long-time velocity in the deterministic limit. The distribution of dissipated heat, however, is non-Gaussian, contrary to the constant-force case.
利用随机热力学框架，我们研究了与由排斥性、非线性、时延反馈驱动的粒子随机运动相关的热产生。最近的研究表明，这种类型的反馈可以在参数空间中的某个阈值之上导致持续运动[R. A. Kopp等人，《物理评论E》107, 024611 (2023)2470 - 004510.1103/PhysRevE.107.024611]。在这里，我们通过数值和解析方法研究了在持续运动阈值附近不同区域的热产生率。我们发现，即使在阈值以下，平均热产生率〈q̇〉也不为零，这表明即使在小反馈情况下系统也具有非平衡特性。在这个区域，我们将其与相应线性化延迟系统以及小延迟近似的解析结果进行比较，后者在小排斥（或延迟时间）时对〈q̇〉提供了合理的描述。超过阈值后，热产生率要大得多，并作为延迟时间的函数呈现出最大值。在这个区域，〈q̇〉可以用一个受到源于确定性极限下长时间速度的恒力作用的系统的热产生率来近似。然而，与恒力情况相反，耗散热的分布是非高斯的。
