  Microscopic physical laws are time-symmetric, hence, a priori there exists no
preferential temporal direction. However, the second law of thermodynamics
allows one to associate the "forward" temporal direction to a positive
variation of the total entropy produced in a thermodynamic process, and a
negative variation with its "time-reversal" counterpart. This definition of a
temporal axis is normally considered to apply in both classical and quantum
contexts. Yet, quantum physics admits also superpositions between forward and
time-reversal processes, whereby the thermodynamic arrow of time becomes
quantum-mechanically undefined. In this work, we demonstrate that a definite
thermodynamic time's arrow can be restored by a quantum measurement of entropy
production, which effectively projects such superpositions onto the forward
(time-reversal) time-direction when large positive (negative) values are
measured. Remarkably, for small values (of the order of plus or minus one), the
amplitudes of forward and time-reversal processes can interfere, giving rise to
entropy-production distributions featuring a more or less reversible process
than either of the two components individually, or any classical mixture
thereof.
