  Fluctuation theorems are relations constraining the out-of-equilibrium
fluctuations of thermodynamic quantities like the entropy production that were
initially introduced for classical or quantum systems in contact with a thermal
bath. Here we show, in the absence of thermal bath, the dynamics of
continuously measured quantum systems can also be described by a fluctuation
theorem, expressed in terms of a recently introduced arrow of time measure.
This theorem captures the emergence of irreversible behavior from microscopic
reversibility in continuous quantum measurements. From this relation, we
demonstrate that measurement-induced wave-function collapse exhibits absolute
irreversibility, 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's
fluorescence.
