In a strong uniform Newtonian gravitational field, the entropy of a monoatomic ideal gas depends on the container's cross-sectional area and is extensive when particle number per unit area is fixed.
The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons
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This letter presents a new, solely thermodynamical argument for considering the states of the quantum isolated horizon of a black hole as distinguishable. We claim that only if the states are distinguishable, the thermodynamic entropy is an extensive quantity and can be well-defined. To show this, we make a comparison with a classical ideal gas system whose statistical description makes only sense if an additional 1/N!-factor is included in the state counting in order to cure the Gibbs paradox. The case of the statistical description of a quantum isolated horizon is elaborated, to make the claim evident.
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A note on entropy of matter in presence of gravity: status of extensivity of entropy
In a strong uniform Newtonian gravitational field, the entropy of a monoatomic ideal gas depends on the container's cross-sectional area and is extensive when particle number per unit area is fixed.