Barrow's black hole entropy and the equipartition theorem

TL;DR

This paper links Barrow's quantum gravitational modified black hole entropy with the equipartition theorem, deriving the entropic exponent and analyzing thermodynamic stability through heat capacity calculations.

Contribution

It establishes a novel relation between Barrow entropy and the equipartition theorem, providing a precise value for the entropic exponent and testing thermodynamic consistency.

Findings

Derived the entropic exponent from equipartition law.

Identified thermodynamically stable range for the Barrow exponent.

Confirmed the consistency of Barrow entropy with black hole thermodynamics.

Abstract

The Barrow entropy appears from the fact that the black hole surface can be modified due to quantum gravitational outcome. The measure of this perturbation is given by a new exponent $\Delta$. In this letter we have shown that, from the standard mathematical form of the equipartition theorem, we can relate it with Barrow entropy. From this equivalence, we have calculated precisely the value of the exponent for the equipartition law. After that, we tested the thermodynamical coherence of the system by calculating the heat capacity which established an interval of the possible thermodynamical coherent values of Barrow entropic exponent and corroborated our first result.