Nonlinear-Maxwell-Yukawa de-Sitter black hole thermodynamics in a cavity: I−Canonical ensemble

We address a complete probe of the phase portrait associated with a nonlinear electrodynamics Maxwell-Yukawa de-Sitter black hole in the canonical ensemble, which signifies that the temperature and the charge on the wall of the cavity are fixed. We start by deriving the free energy with the help of the Euclidean action calculation of general nonlinear electrodynamics in the presence of the cosmological constant. We also ensure that the first law of thermodynamics is satisfied. Within the Yukawa nonlinear electrodynamics, we discuss the Hawking-Page-like phase transition occurring in the weak scheme. In the strong scheme, we observe a Waals-like phase picture, which is not detected in absence of the cavity 1. Finally, a special emphasis has been put on the examination of the extremal case within the Yukawa parameter α.