Mechanical work extraction from an error-prone active dynamic Szilard engine

Isothermal information engines operate by extracting net work from a single heat bath through measurement and feedback control. In this work, we analyze a realistic active Szilard engine operating on a single active particle by means of steric interaction with an externally controlled mechanical element. In particular, we provide a comprehensive study of how finite measurement accuracy affects the engine's work and power output, as well as the cost of operation. Having established the existence of non-trivial optima for work and power output, we study the dependence of their loci on the measurement error parameters and identify conditions for their positivity under one-shot and cyclic engine operation. By computing a suitably defined information efficiency, we also demonstrate that this engine design allows for the violation of Landauer's bound on the efficiency of information-to-work conversion. Notably, the information efficiency for one-shot operation exhibits a discontinuous transition and a non-monotonic dependence on the measurement precision. Finally, we show that cyclic operation improves information efficiency by harvesting residual mutual information between successive measurements.