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Active particles in moving traps: Minimum work protocols and information efficiency of work extraction

Janik Schüttler1, Rosalba Garcia-Millan1,2,3, Michael E. Cates1, and Sarah A. M. Loos1,4,*

  • *Contact author: sl2127@cam.ac.uk
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Phys. Rev. E 112, 024119 – Published 18 August, 2025

DOI: https://doi.org/10.1103/4q4f-1dpx

Abstract

We revisit the elementary problem of moving a particle in a harmonic trap in finite time with minimal work cost and extend it to the case of an active particle. By comparing the Gaussian case of an Active Ornstein-Uhlenbeck particle and the non-Gaussian run-and-tumble particle, we establish general principles for thermodynamically optimal control of active matter beyond specific models. We show that the open-loop optimal protocols, which do not incorporate system-state information, are identical to those of passive particles but result in larger work fluctuations due to activity. In contrast, closed-loop (or feedback) control with a single (initial) measurement changes the optimal protocol and reduces the average work relative to the open-loop control for small enough measurement errors. Minimum work is achieved by particles with finite persistence time. As an application, we propose an active information engine which extracts work from self-propulsion. This periodic engine achieves higher information efficiency with run-and-tumble particles than with active Ornstein-Uhlenbeck particles. Complementing a companion paper that gives only the main results [Garcia-Millan et al., companion paper, Phys. Rev. Lett. 135, 088301 (2025)], here we provide a full account of our theoretical calculations and simulation results. We include derivations of optimal protocols, work variance, impact of measurement uncertainty, and information-acquisition costs.

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Optimal Closed-Loop Control of Active Particles and a Minimal Information Engine

Rosalba Garcia-Millan, Janik Schüttler, Michael E. Cates, and Sarah A. M. Loos
Phys. Rev. Lett. 135, 088301 (2025)

Article Text

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Outline

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Phys. Rev. E 112, 024119– Published 18 August, 2025
  • Received 24 January 2025
  • Accepted 9 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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