Gibbs' paradox and black-hole entropy

Details Gibbs' paradox and black-hole entropy Gibbs' paradox and black-hole entropy

2007-07-04

arxiv.org/abs/0707.0615v1

Gen.Rel.Grav.40:1327-1339,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Contribution to Mashhoon festschrift, 13 pages, 4 figures

Scientific paper

10.1007/s10714-008-0609-5

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.

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