GUP corrections to black hole thermodynamics in the extended phase-space approach

In this work, we study corrections to black hole (BH) temperature and entropy in the context of the generalized uncertainty principle. In particular, we obtain corrected asymptotically Anti-de Sitter BH solutions following the extended phase-space scheme in which the cosmological constant is considered as a thermodynamic pressure satisfying certain equation of state (EoS). Among all the possibilities, we consider that the cosmological pressure satisfies either a polytropic or a Chaplygin EoS. The physical plausibility of the solutions is studied based on the energy conditions and the associated heat capacity.