Heat production in a stochastic system with nonlinear time-delayed feedback
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915183562063872 |
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| author | Kopp, Robin A. Klapp, Sabine H. L. |
| author_facet | Kopp, Robin A. Klapp, Sabine H. L. |
| contents | 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 [Physical Review E 107, 024611 (2023)]. 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, $\langle \dot{q}\rangle$, 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 $\langle \dot{q}\rangle$ at small repulsion (or delay time). Beyond the threshold, the rate of heat production is much larger and shows a maximum as function of the delay time. In this regime, $\langle \dot{q}\rangle$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heat production in a stochastic system with nonlinear time-delayed feedback Kopp, Robin A. Klapp, Sabine H. L. Soft Condensed Matter Statistical Mechanics 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 [Physical Review E 107, 024611 (2023)]. 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, $\langle \dot{q}\rangle$, 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 $\langle \dot{q}\rangle$ at small repulsion (or delay time). Beyond the threshold, the rate of heat production is much larger and shows a maximum as function of the delay time. In this regime, $\langle \dot{q}\rangle$ 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. |
| title | Heat production in a stochastic system with nonlinear time-delayed feedback |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2408.03316 |