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Fluctuation theorems are relations constraining the out-of-equilibriumfluctuations of thermodynamic quantities like the entropy production that wereinitially introduced for classical or quantum systems in contact with a thermalbath. Here we show, in the absence of thermal bath, the dynamics ofcontinuously measured quantum systems can also be described by a fluctuationtheorem, expressed in terms of a recently introduced arrow of time measure.This theorem captures the emergence of irreversible behavior from microscopicreversibility in continuous quantum measurements. From this relation, wedemonstrate that measurement-induced wave-function collapse exhibits absoluteirreversibility, such that Jarzynski and Crooks-like equalities are violated.We apply our results to different continuous measurement schemes on a qubit:dispersive measurement, homodyne and heterodyne detection of a qubit'sfluorescence.

Fluctuation Theorems for Continuous Quantum Measurement and Absolute Irreversibility