General Relativity and Gravitation

, Volume 40, Issue 6, pp 1327–1339

Gibbs’ paradox and black-hole entropy

Research Article

DOI: 10.1007/s10714-008-0609-5

Cite this article as:
Kiefer, C. & Kolland, G. Gen Relativ Gravit (2008) 40: 1327. doi: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.


Black-hole entropyLogarithmic correctionsQuantum gravity

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität zu KölnCologneGermany