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In the context of Black Hole Chemistry (BHC), holographic phase transitionsof asymptotically anti-de Sitter (AdS) charged topological black holes (TBHs)in massive gravity coupled to Power Maxwell Invariant (PMI) electrodynamics arediscussed in the grand canonical (fixed $U(1)$ potential, $\Phi$) ensemble.Considering all higher-order graviton's self-interactions of (dRGT) massivegravitational field theory in arbitrary dimensions, exact TBH solutions arederived, the explicit form of the on-shell action is computed, and theassociated thermodynamic quantities in the Grand Canonical Ensemble (GCE) arecalculated. In addition, the validity of the first law of thermodynamics andSmarr relation are examined in the extended phase space. Regarding this model,it is shown that a van der Waals (vdW) behavior takes place in $d \ge 4$dimensions, a typical reentrant phase transition is observed in $d \ge 5$, andboth anomalous vdW and triple point phenomena are recognized in $d \ge 6$. So,the results are quite different from their counterparts in the GCE ofMaxwell-massive gravity. Besides, we briefly study the critical behaviors ofhigher-dimensional TBHs with a conformally invariant Maxwell source as aspecial subgroup of our solutions for both Einstein and massive gravitytheories in various ensembles.

Nonlinearly Charged Black Hole Chemistry with Massive Gravitons in the Grand Canonical Ensemble