Gibbs' paradox and black-hole entropy

Understand

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.