Loop Quantum Gravity Immirzi parameter and the Kaniadakis statistics

TL;DR

This paper explores how different non-extensive thermostatistics, specifically Kaniadakis and Tsallis statistics, influence the calculation of the Immirzi parameter in Loop Quantum Gravity, revealing new relations and connections.

Contribution

It introduces a novel relation between the Immirzi parameter, Kaniadakis kappa, and surface area, extending previous work with Tsallis statistics.

Findings

Derived a new relation between Immirzi parameter, Kaniadakis kappa, and surface area.

Compared Kaniadakis and Tsallis statistics in the context of LQG.

Showed that the Immirzi parameter can be used to relate different non-Gaussian statistics.

Abstract

In this letter we have shown that a possible connection between the LQG Immirzi parameter and the area of a punctured surface can emerge depending on the thermostatistics theory previously chosen. Starting from the Boltzmann-Gibbs entropy, the Immirzi parameter can be reobtained. Using the Kaniadakis statistics, which is an important non-Gaussian statistics, we have derived a new relation between the Immirzi parameter, the kappa parameter and the area of a punctured surface. After that, we have compared our result with the Immirzi parameter previously obtained in the literature within the context of Tsallis' statistics. We have demonstrated in an exact way that the LQG Immirzi parameter can also be used to compare both Kaniadakis and Tsallis statics.