Thermodynamics and phase transition of Bardeen black hole via Rényi statistics in grand canonical ensemble and canonical ensemble

Abstract

Abstract The thermodynamics of the Bardeen black hole in asymptotically flat space is investigated with the corrected first law of thermodynamics via Rényi statistics. The nonextensive parameter $$\lambda $$ λ gives the possibility to the thermal stability of Bardeen black hole, and there is a Hawking–Page phase transition in the grand canonical ensemble (fixed the potential), which is similar to the cases of Bardeen black hole and corrected Bardeen black hole in asymptotically anti-de Sitter (AdS) space via standard Gibbs–Boltzmann (GB) statistics. By introducing the general Smarr formula via Rényi statistics, the thermodynamic pressure P is defined with the parameter $$\lambda $$ λ and its conjugate quantity V is the thermodynamic volume (not a geometric spherical volume with horizon radius $$r_{h}$$ r h ). The thermodynamics of the asymptotically flat Bardeen black hole via Rényi statistics in the canonical ensemble (fixed the charge q) behaves like the van der Waals system, which is also same as the asymptotically Bardeen-AdS black hole via GB statistics. The analogy between the thermodynamics of the asymptotically flat Bardeen black hole from Rényi statistics and the Bardeen-AdS black hole from GB statistics makes us to consider what is the relation between the nonextensive parameter $$\lambda $$ λ and the cosmological constant $$\Lambda $$ Λ .