Critical phenomena of charged dilatonic black holes through Rényi statistics approach

Abstract

In this paper, in order to describe the non-Boltzmannian phase structure of charged dilatonic black holes in the absence of the cosmological constant, we consider the Rényi statistics as an extension of the Boltzmann–Gibbs theory which also satisfies Abe’s formula. This description is achieved by considering such a black hole either as a closed system (canonical ensemble) or as an open system (grand canonical ensemble). Through this study, we find that a Hawking–Page phase transition and a Van der Waals phase portrait appear within the grand canonical ensemble and canonical ensemble, respectively, these transitions are absent in the usual Boltzmann–Gibbs’s description. Furthermore, such phase structures provide another example wherein the thermodynamics associated with a vanishing cosmological constant black holes via Rényi statistics processes the same proprieties as those of asymptotically AdS charged black holes via Gibbs–Boltzmann formalism. This provides more insight into a possible and deep connection between the nonextensive Rényi parameter [Formula: see text] and the cosmological constant [Formula: see text]. Among others, we have addressed a generalization of [C. Promsiri, E. Hirunsirisawat and W. Liewrian, Phys. Rev. D 102 (2020) 064014] to dilaton gravity background and [R. Zhao, H.-H. Zhao, M.-S. Ma and L.-C. Zhang, Eur. Phys. J. C 73 (2013) 2645] to Rényi statistics approach.