Quantum mechanics gives new insights into the Gibbs paradox
"The classical Gibbs paradox
The classical Gibbs paradox takes the form of a thought experiment involving a box with a partition that separates two bodies of gas. When the partition is removed, the two gas bodies mix spontaneously. To an informed observer who can distinguish the two gas bodies, the system’s entropy increases. On the other hand, for an ignorant observer who cannot discern any differences between the two gas bodies, there is no visible mixing and the entropy remains unchanged.
This difference of opinion has a physical significance since work can be extracted through the mixing process when the entropy increases. That suggests that the system’s entropy should be an objective quantity – something that does not reconcile with the existence of the different outcomes for the two observers. Gibbs, however, noted that the extraction of work depends on the experimental apparatus of the observer. Hence, the informed observer can extract work, whereas the ignorant observer has to contend with their inability to do so. This makes each observer’s reality consistent with the entropy change they witness."
In the new work, the Oxford-Nottingham team considered how quantum effects such as superposition would affect the thought experiment. As in the classical case, the informed observer witnesses an entropy increase. For the ignorant observer, however, there is a marked difference after transitioning to the quantum realm. Although they are still unable to distinguish the two gases, they, too, can now witness an entropy increase. At the macroscopic limit, this entropy increase can even become as large as that which the informed observer perceives, providing the maximal discrepancy to the classical case."