  We provide mass/energy formulas for the extended thermodynamics, mixed
thermodynamics, and holographic conformal field theory (CFT) thermodynamics for
the charged and rotating Kerr-Newman Anti-de Sitter black holes. Then for the
CFT thermal states dual to the black hole, we find the first-order phase
transitions and criticality phenomena in the canonical ensemble with fixed
angular momentum, volume, and central charge. We observe that the CFT states
cannot be analogous to the Van der Waals fluids, despite the critical exponents
falling into the universality class predicted by the mean field theory.
Additionally, we examine the (de)confinement phase transitions within the grand
canonical ensemble with fixed angular velocity, volume, and central charge of
the CFT. Our findings suggest that the near zero temperature (de)confinement
phase transitions can occur with the angular velocity of the CFT that solely
depends on the CFT volume.
