Thermodynamics of charged anti-de Sitter black holes in canonical ensemble

As in the grand canonical treatment of Reissner - Nordstr\"{o}m black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes.