The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons

TL;DR

This paper argues that quantum isolated horizon states of black holes are distinguishable, ensuring thermodynamic entropy is extensive, by drawing an analogy with classical ideal gases and addressing the Gibbs paradox.

Contribution

It introduces a thermodynamical argument for the distinguishability of black hole horizon states, linking quantum horizon entropy to classical statistical mechanics principles.

Findings

States of quantum isolated horizons are distinguishable.

Thermodynamic entropy of horizons is extensive.

Comparison with classical ideal gas clarifies the role of state counting.

Abstract

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.