Optimal work control for an odd-diffusive tracer under active fluctuations

We investigate optimal work protocols for a tracer particle with odd mobility, confined in a rotationally asymmetric parabolic potential, and driven by temporally correlated (active) noise originating from an active process. Two control strategies are considered: open loop (without measurement of the initial active force) and closed loop (with measurement-based feedback). In the open-loop case, neither activity nor odd mobility affects the average optimal work; however, the potential asymmetry enables the work extraction, and the oddness parameter <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>κ</a:mi> </a:math> shapes the protocol structure—introducing asymmetries and even backward jumps at the initial and final times. In the closed-loop setting, both activity and odd mobility shape the protocol design to enable work extraction. Optimal protocols exhibit directional asymmetries, including discontinuities and reversals, which depend on the alignment of the initial active force and the persistence time. Maximum work extraction occurs when the initial force aligns with the target at an intermediate persistence time, even in symmetric potentials. Furthermore, in regimes where such alignment disfavors work extraction for a normal tracer, odd mobility facilitates it. These findings highlight the potential for energy harvesting in active systems, driven by feedback and asymmetric interactions between different degrees of freedom.