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

## TL;DR

This paper derives the black hole entropy law using non-extensive statistical mechanics within loop quantum gravity, linking the Barbero-Immirzi parameter to horizon microstate bias and suggesting experimental determination to fix the theory.

## Contribution

It introduces a novel approach connecting non-extensive statistics with quantum geometric microstates, generalizing the entropy calculation for all positive Barbero-Immirzi parameters.

## Key findings

- Derivation of Bekenstein-Hawking law from non-extensive statistics
- Encoding of Barbero-Immirzi parameter as horizon microstate bias
- Proposal for experimental determination of the parameter

## Abstract

Using non-extensive statistical mechanics, the Bekenstein-Hawking area law is obtained from microstates of black holes in loop quantum gravity, for arbitrary real positive values of the Barbero-Immirzi parameter$(\gamma)$. The arbitrariness of $\gamma$ is encoded in the strength of the "bias" created in the horizon microstates through the coupling with the quantum geometric fields exterior to the horizon. An experimental determination of $\gamma$ will fix this coupling, leaving out the macroscopic area of the black hole to be the only free quantity of the theory.