Mixing indistinguishable systems leads to a quantum Gibbs paradox

TL;DR

This paper explores a quantum analogue of the Gibbs paradox, showing that an uninformed observer can extract work from mixing indistinguishable quantum gases, revealing fundamental differences from classical thermodynamics.

Contribution

It introduces a quantum version of the Gibbs paradox, demonstrating that ignorance affects entropy and work extraction in quantum systems, diverging from classical expectations.

Findings

Ignorant observers can extract work from quantum gas mixing.

Quantum systems show divergence from classical thermodynamics in the macroscopic limit.

More microstates are assigned by the observer than in naive semiclassical counting.

Abstract

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