Fig. 1: The Gibbs paradox. | Nature Communications

Fig. 1: The Gibbs paradox.

From: Mixing indistinguishable systems leads to a quantum Gibbs paradox

Fig. 1

Two distinct gases of n particles at the same temperature and pressure are separated by a partition. This partition is removed and the gases are allowed to mix and reach equilibrium. Two observers calculating the entropy increase during the process disagree depending on their ability to distinguish the particles. An informed observer, who can measure the difference between the gases, calculates \(2n\,{\mathrm{ln}}\,2\), while an observer ignorant of the difference records no entropy change. In this work, we ask how the situation changes when classical particles are replaced by identical quantum particles.

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