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Thermodynamics of quantum coherence has attracted growing attention recently,where the thermodynamic advantage of quantum superposition is characterized interms of quantum thermodynamics. We investigate thermodynamic effects ofquantum coherent driving in the context of the fluctuation theorem. We adopt aquantum-trajectory approach to investigate open quantum systems under feedbackcontrol. In these systems, the measurement backaction in the forward processplays a key role, and therefore the corresponding time-reversed quantummeasurement and post-selection must be considered in the backward process insharp contrast to the classical case. The state reduction associated withquantum measurement, in general, creates a zero-probability region in the spaceof quantum trajectories of the forward process, which causes singularly strongirreversibility with divergent entropy production (i.e., absoluteirreversibility) and hence makes the ordinary fluctuation theorem break down.In the classical case, the error-free measurement ordinarily leads to absoluteirreversibility because the measurement restricts classical paths to the regioncompatible with the measurement outcome. In contrast, in open quantum systems,absolute irreversibility is suppressed even in the presence of the projectivemeasurement due to those quantum rare events that go through the classicallyforbidden region with the aid of quantum coherent driving. This suppression ofabsolute irreversibility exemplifies the thermodynamic advantage of quantumcoherent driving. Absolute irreversibility is shown to emerge in the absence ofcoherent driving after the measurement, especially in systems undertime-delayed feedback control. We show that absolute irreversibility ismitigated by increasing the duration of quantum coherent driving or decreasingthe delay time of feedback control.

Fluctuation theorems in feedback-controlled open quantum systems: quantum coherence and absolute irreversibility