Using the restricted phase space (RPST) formalism, we perform a comparative study of 4D dyonic AdS black hole thermodynamics in Gibbs–Boltzmann statistics and Rényi statistics. In RPST formalism, instead of pressure and volume, one considers central charge C and chemical potential \(\mu \) as thermodynamic variables. 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 in the T–S processes and a Hawking–Page and Davies type phase transition in the F–T and specific heat plots on top of the Van der Waals and superfluid \(\lambda \) phase transitions. 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 meaning for isovoltage processes we see Hawking–Page transition in Bekenstein–Hawking entropy and absence of Hawking–Page in Rényi entropy construct. We observe an interesting phenomenon where changing the Rényi 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. 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. Finally, we do not see a new universality class for modified entropy as it is seen in studies done for alternate gravity models.
