Noncommutative black holes in extended anti-de Sitter phase space

We study thermodynamic aspects of ordinary and lower dimensional noncommutative black holes within an extended anti-de Sitter phase space by treating the negative cosmological constant and the minimal cut-off length as thermodynamic variables representing the pressure and tension of the system, respectively. In four-dimensional spacetime, the regular black hole exhibits a small/large black hole phase transition analogous to the liquid/gas transition of a Van der Waals gas. The three-dimensional case demonstrates global and local thermodynamic stability, while the two-dimensional case reveals a novel type of transition referred to as the anti-Hawking-Page transition.