Exploring critical behavior of thermodynamic variables of the Kerr-Newman-AdS black hole in the restricted phase space

The present work investigates the thermodynamic properties of the four-dimensional Kerr-NewmannAdS black hole, utilizing the recently proposed framework of restricted phase space thermodynamics. This approach introduces a novel set of paired thermodynamic variables; the central charge (C) of the corresponding dual conformal field theory and the chemical potential (mu). Through rigorous analysis, we establish fundamental relationships, including the Euler relation, Gibbs-Duhem relation, and the zerothorder homogeneity of intensive variables. Furthermore, numerical techniques are employed to explore thermodynamic processes between the conjugate variables in canonical and grand canonical ensembles. Our investigation reveals first-order and second-order phase transitions across various macroscopic processes. Despite the absence of complete analytical expressions, our findings unveil striking similarities in behavior between Reissner-Nordstr & ouml;m-Anti-de Sitter and Kerr-anti-de Sitter, underscoring the presence of underlying universality within the restricted phase space thermodynamics formalism.