  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 Szilard
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 excess entropy production. The study considers different measurement
scenarios, highlighting the role of measurement precision in determining engine
efficiency.
