Nonlinearly charged black hole chemistry with massive gravitons in the grand canonical ensemble

the context of black hole chemistry (BHC), holographic phase transitions of asymptotically antide Sitter (AdS) charged topological black holes (TBHs) in massive gravity coupled to power Maxwell invariant (PMI) electrodynamics are discussed in the grand canonical (fixed U(1) potential, Phi) ensemble. Considering the higher-order of graviton's self-interactions of (dRGT) massive gravitational field theory in arbitrary dimensions, we derive exact TBH solutions. We also calculate the explicit form of the on-shell action and the associated thermodynamic quantities in the grand canonical ensemble (GCE). Besides, we examine the validity of the first law of thermodynamics and Smarr relation in the extended phase space thermodynamics. Regarding this model, we show that (a) a van der Waals (vdW) behavior takes place in d >= 4 dimensions, (b) a typical reentrant phase transition can happen in d >= 5, and (c) both anomalous vdWand triple point phenomena are recognized in d >= 6. Accordingly, we find that the obtained results are quite different from their counterparts in the GCE of Maxwell-massive gravity. Furthermore, we briefly study the critical behaviors of higher-dimensional TBHs with a conformally invariant Maxwell source as a specific subclass of our solutions for Einstein's theory and the massive gravity in various ensembles.