Restricted Phase Space Thermodynamics of Dyonic AdS Black Holes: Comparative Analysis Using Different Entropy Models

We study the Restricted Phase Space Thermodynamics (RPST) for the AdS dyonic black hole carrying the central charge $C$ and the chemical potential $\mu$, neglecting the pressure and conjugate volume along with comparison of different entropy models namely the Bekenstein-Hawking and the R\'enyi entropy model. Inclusion of the magnetic charge $\tilde{Q}_m$ gives rise to a richer phase structure of the study of thermodynamics by adding a non-equilibrium transition from an unstable small black hole to a stable black hole on top of the Van der Waals transition in the $T-S$ processes and a Hawking-Page transition in the $F-T$ plots. We study an extra mixed ensemble ($\tilde{\Phi}_e,\tilde{Q}_m)$ due to the inclusion of $\tilde{Q}_m$ where we see Van der Waals phase transition and whose plots change as the entropy model changes though the style of transition remains the same. We observe an interesting phenomenon where changing the R\'enyi parameter $\lambda$, the $T-S$ process changes the same way as when varying the central charge $C$ underlining some similarity that is not seen in the Bekenstein Hawking entropy model. We observe a similarity between the plots when both charges are turned off relating to the Schwarzschild black hole and the grand-canonical ensemble. One can observe that as the entropy models are changed, the homogeneity is not lost where the mass as a function of extensive variables is of order one and the rest zero. Finally, we see a similarity in the $\mu-C$ process across the entropy models signally some universality across entropy models as well as different types of black holes studied before.