Quantum fluctuation relations in first-detection processes

This paper investigates the thermodynamics of quantum information engines that operate based on first-detection protocols. Specifically, it seeks to establish fundamental bounds on the work that can be extracted when a feedback controller (or "demon") performs repeated projective measurements and triggers a mechanical operation only upon the first occurrence of a specific measurement outcome.

The author employs the framework of quantum thermodynamics to analyze systems undergoing stroboscopic projective measurements. By defining the first-detection probability and the corresponding post-measurement states, the study derives two distinct fluctuation relations: one for the total energy change during the measurement-and-feedback sequence, and another for the work extracted by the final operation alone. These relations are derived by comparing the forward dynamics of the engine to a time-reversed process, where the correction to the standard Jarzynski equality is expressed through the mean first-detection time of the time-reversed dynamics.

The study establishes that the information gained through stroboscopic measurements acts as a thermodynamic resource that modifies the standard Jarzynski equality. By applying Jensen's inequality to these new fluctuation relations, the author derives rigorous lower bounds on the total work cost and upper bounds on the extractable work. Furthermore, the paper introduces an "average ergotropy" as an additional figure of merit, demonstrating that it provides a tighter or more general upper bound on the performance of the engine compared to the bounds derived from the fluctuation relations alone. The results are illustrated using a two-spin model, showing how the sampling interval of the measurements influences the extracted power.