Machine-learning-derived protocols for information-based work extraction from active particles

We propose and analyze a process that extracts useful work from a single active particle maintained at constant temperature in a harmonic potential by measuring the relative sign of the self-propulsion and the confining force and then adjusting the stiffness of the potential. First, we show analytically that useful work can be extracted by stepwise changes of the stiffness. Then, we use a machine learning procedure to find time-dependent stiffness change protocols. We find that these protocols involve discontinuous initial changes of the stiffness opposite to the expected direction, which resemble initial jumps analytically found by Garcia-Millan et al. [Phys. Rev. Lett. 135, 088301 (2025)] in a different information-based work extraction process. The learned protocols allow to extract significantly larger amounts of useful work. The work extracted exceeds that allowed by the conventional second law for feedback-controlled processes, which can be rationalized by the non-equilibrium character of the system considered.