The superpositions of thermodynamical arrows of time

[1] Time’s Arrow of a Quantum Superposition of Thermodynamic Evolutions. By G. Rubino , G. Manzano, and C. Brukner 

Fundamental laws of physics are generally time-symmetric. The directionality of time is then often explained with the thermodynamic arrow of time: the entropy of an isolated system increases during a process, and it is constant only if the process is reversible. For example, if we bring a hot object into contact with a cold object, we observe that the hot object cools down and the cold warms up, but never the opposite.

In [1] we consider a quantum superposition between two processes with opposing thermodynamic arrows of time. How is then a definite arrow of time established for such a superposition? We show that a quantum measurement of entropy change (for values larger than the thermal fluctuations) can be accountable for this. In particular, while the individual result of the measurement is random, once the value of the entropy variation has been observed, the system continues its evolution according to a definite arrow of time. However, for entropy variations lower than (or of the order of) the thermal fluctuations, interference effects can cause entropy changes which are classically impossible.