Revisiting the Immirzi parameter: Landauer’s principle and alternative entropy frameworks in loop quantum gravity

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, $$\gamma = \ln 2/(\pi \sqrt{3})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>=</mml:mo> <mml:mo>ln</mml:mo> <mml:mn>2</mml:mn> <mml:mo>/</mml:mo> <mml:mo>(</mml:mo> <mml:mi>π</mml:mi> <mml:msqrt> <mml:mn>3</mml:mn> </mml:msqrt> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , 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.