Loop Quantum Gravity Immirzi parameter and the Kaniadakis statistics

Understand

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.