Gibbs' paradox and black-hole entropy

TL;DR

The paper explores how the concept of indistinguishability in statistical mechanics explains the derivation of black-hole entropy and its quantum corrections, drawing parallels with Gibbs' paradox.

Contribution

It demonstrates the analogy between Gibbs' paradox and black-hole entropy, clarifies the role of indistinguishability in quantum gravity approaches, and explains logarithmic entropy corrections.

Findings

Indistinguishability assumptions affect black-hole entropy calculations.

Logarithmic corrections to entropy can be understood through standard statistical mechanics.

The area quantization model illustrates the concepts effectively.

Abstract

In statistical mechanics Gibbs' paradox is avoided if the particles of a gas are assumed to be indistinguishable. The resulting entropy then agrees with the empirically tested thermodynamic entropy up to a term proportional to the logarithm of the particle number. We discuss here how analogous situations arise in the statistical foundation of black-hole entropy. Depending on the underlying approach to quantum gravity, the fundamental objects to be counted have to be assumed indistinguishable or not in order to arrive at the Bekenstein--Hawking entropy. We also show that the logarithmic corrections to this entropy, including their signs, can be understood along the lines of standard statistical mechanics. We illustrate the general concepts within the area quantization model of Bekenstein and Mukhanov.