Versatile Thermodynamics Study of $F(R)$ Gravity Corrected Black Holes Through Generalized Entropy

In this paper, we investigate the thermodynamic properties and geometries of phantom $(A)dS$ $F(R)$ black holes in the presence of recently proposed generalized entropy. For this purpose, we evaluate the heat capacity, Helmholtz free energy, Gibbs free energy, compressibility factor Z and the isothermal compressibility (κT) for analyzing the local and global stability of this black hole. We also analyze the thermal geometries of this black hole, which provide useful insights. Furthermore, we present isotherms on the P-V diagram illustrating phase behavior. It is interesting to mention here that generalized entropy provide significant and useful impact on the results of thermal analysis of aforementioned black holes.