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

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.