Efficiency of an autonomous, dynamic information engine operating on a single active particle.

The Szilard engine stands as a compelling illustration of the intricate interplay between information and thermodynamics. While at thermodynamic equilibrium, the apparent breach of the second law of thermodynamics was reconciled by Landauer and Bennett's insights into memory writing and erasure, recent extensions of these concepts into regimes featuring active fluctuations have unveiled the prospect of exceeding Landauer's bound, capitalizing on information to divert free energy from dissipation towards useful work. To explore this question further, we investigate an autonomous dynamic information engine, addressing the thermodynamic consistency of work extraction and measurement costs by extending the phase space to incorporate an auxiliary system, which plays the role of an explicit measurement device. The nonreciprocal coupling between active particle and measurement device introduces a feedback control loop, and the cost of measurement is quantified through a suitably defined auxiliary entropy production. The study considers different measurement scenarios, highlighting the role of measurement precision in determining engine efficiency.