Mixing indistinguishable systems leads to a quantum Gibbs paradox

The classical Gibbs paradox concerns the entropy change upon mixing two gases. Whether an observer assigns increase to process depends on their ability distinguish A resolution is that "ignorant" observer, who cannot gases, has no way of extracting work by them. Moving thought experiment into quantum realm, we reveal new and surprising behaviour: ignorant can extract from different even if gases be directly distinguished. Moreover, in macroscopic limit, case diverges ideal gas: as much extracted were fully distinguishable. We show more microstates system than found naive counting semiclassical statistical mechanics. This demonstrates importance accounting for level knowledge its implications genuinely modifications thermodynamics.