Revisiting the Immirzi parameter: Landauer's principle and alternative entropy frameworks in Loop Quantum Gravity

TL;DR

This paper uses Landauer's principle and alternative entropy frameworks to derive the Immirzi parameter in Loop Quantum Gravity, providing new insights into black hole entropy and thermodynamics without relying on traditional Boltzmann-Gibbs entropy.

Contribution

It introduces a novel approach to determine the Immirzi parameter using thermodynamic principles and alternative entropy formulations in Loop Quantum Gravity.

Findings

Derived the standard Immirzi parameter using Landauer's principle.

Extended the derivation to Barrow's entropy formulation.

Obtained a new expression for the Immirzi parameter with Kaniadakis entropy.

Abstract

This paper investigates the implications from area quantization in Loop Quantum Gravity, particularly focusing on the application of the Landauer principle -- a fundamental thermodynamic concept establishing a connection between information theory and thermodynamics. By leveraging the Landauer principle in conjunction with the Bekenstein-Hawking entropy law, we derive the usual value for the Immirzi parameter precisely, $\gamma = \ln2/(\pi \sqrt{3})$, without using the typical procedure that involves the Boltzmann-Gibbs entropy. Furthermore, following an analogous procedure, we derive a modified expression for the Immirzi parameter aligned with Barrow's entropy formulation. Our analysis also yields a new expression for the Immirzi parameter consistent with a corresponding modified Kaniadakis entropy for black hole entropy further illustrating, along with Barrow's entropy, the applicability of Landauer's principle in alternative statistical contexts within black hole physics.