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

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.

8 pages, closest to the published version; taken from the author's diploma thesis

References in corpus (8)

• Counting black hole microscopic states in loop quantum gravity
• The combinatorics of the SU(2) black hole entropy in loop quantum gravity
• Gibbs' paradox and black-hole entropy
• Generic isolated horizons in loop quantum gravity
• Fine-grained state counting for black holes in loop quantum gravity
• Comment on "Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?" by B. Dittrich and T. Thiemann
• Radiation from quantum weakly dynamical horizons in LQG
• Entropy of Quantum Black Holes

Cited by in corpus (5)

• Statistics, holography, and black hole entropy in loop quantum gravity
• Anyonic statistics and large horizon diffeomorphisms for Loop Quantum Gravity Black Holes
• Aspects of quantum gravity
• A note on entropy of matter in presence of gravity: status of extensivity of entropy
• A note on electrical and thermodynamic properties of Isolated Horizon