Is The Internal Entropy of F(R)-Gravity Really An Entropy?

TL;DR

This paper compares two methods for deriving entropy functionals in F(R)-Gravity, revealing a discrepancy in the internal entropy component between the functional approach and conventional methods.

Contribution

It demonstrates an incompatibility between the internal entropy derived from the entropy functional and the conventional approach in F(R)-Gravity.

Findings

The entropy functional can be separated into two parts.

The internal entropy from the functional approach differs from the conventional method.

The paper highlights a fundamental inconsistency in the interpretation of internal entropy.

Abstract

This paper connects two methods for finding the functional of entropy in F(R)-Gravity: Padmanabhan's and Hammad's. The resulting approach is simple to follow and yields entropy functional, which can be separated into two parts. The part unknown in General Relativity is often called in the literature as an internal entropy and this paper points on incompatibility between the internal entropy found from the entropy functional and the one found using conventional approach.