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

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