Non-extensive Statistical Mechanics and Black Hole Entropy From Quantum Geometry

Abhishek Majhi (ICN-UNAM)

We apply non-extensive statistical mechanics, characterized by a free parameter $q$, to calculate black hole entropy from quantum geometry. For a given horizon area, the entropy of the black hole is given by the Bekenstein-Hawking area law for arbitrary real positive values of the Barbero-Immirzi parameter($\gamma$). In the process, we find a specific correlation between $\gamma$ and $q$ that explains how the Chern-Simons gauge fields on the horizon is coupled to the bulk geometry exterior to the horizon. It precisely comes out to be such that the microstates of the horizon become more biased away from occurring with equal probability with the increasing strength of the coupling. In passing, we deduce the non-additive entropy for a system of $N$ number of spins with arbitrary spin quantum numbers which can have applications in other fields related to quantum physics than back holes.