Time's Arrow of a Quantum Superposition of Thermodynamic Evolutions

A priori, there exists no preferential temporal direction as microscopic physical laws are time-symmetric. Still, 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, thereby seemingly eluding conventional definitions of time's arrow. In this talk, I will demonstrate that a quantum measurement of entropy production can distinguish the two temporal directions, effectively projecting such superpositions of thermodynamic processes 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.
Finally, I will extend these concepts to the case of a thermal machine running in a superposition of the heat engine and the refrigerator mode, illustrating how such interference effects can be employed to reduce undesirable fluctuations.