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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2602.13173 |
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| _version_ | 1866910021675122688 |
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| author | Welker, Till Pietzonka, Patrick |
| author_facet | Welker, Till Pietzonka, Patrick |
| contents | How much work does it cost for a propelled particle to stay localised near a stationary target, defying both thermal noise and a constant flow that would carry it away? We study the control of such a particle in finite time and find optimal protocols for time-dependent swim velocity and diffusivity, without feedback. Accuracy, quantified via the mean squared deviation from the target, and energetic cost turn out to be related by a trade-off, which complements the one between precision and cost known in stochastic thermodynamics. We show that accuracy better than a certain threshold requires active driving, which comes at a cost that increases with accuracy. The optimal protocols have discontinuous swim velocity and diffusivity, switching between a passive drift state with vanishing diffusivity and an active propulsion state. This study highlights how a time-dependent diffusivity enhances optimal control and sets benchmarks for cost and accuracy of artificial self-propelled particles navigating noisy environments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13173 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Accuracy Comes at a Cost: Optimal Localisation Against a Flow Welker, Till Pietzonka, Patrick Statistical Mechanics How much work does it cost for a propelled particle to stay localised near a stationary target, defying both thermal noise and a constant flow that would carry it away? We study the control of such a particle in finite time and find optimal protocols for time-dependent swim velocity and diffusivity, without feedback. Accuracy, quantified via the mean squared deviation from the target, and energetic cost turn out to be related by a trade-off, which complements the one between precision and cost known in stochastic thermodynamics. We show that accuracy better than a certain threshold requires active driving, which comes at a cost that increases with accuracy. The optimal protocols have discontinuous swim velocity and diffusivity, switching between a passive drift state with vanishing diffusivity and an active propulsion state. This study highlights how a time-dependent diffusivity enhances optimal control and sets benchmarks for cost and accuracy of artificial self-propelled particles navigating noisy environments. |
| title | Accuracy Comes at a Cost: Optimal Localisation Against a Flow |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2602.13173 |