Thermodynamic schemes of charged BTZ-like black holes in arbitrary dimensions

We investigate thermodynamic schemes of charged BTZ-like black holes in arbitrary dimensions, namely higher-dimensional charged black holes in which the electromagnetic sector exhibits the same properties with that of the usual three-dimensional BTZ solution. We first present the Euclidean on-shell action in arbitrary dimensions, inserting a radial cutoff. We then extract the corresponding thermodynamic quantities from the semi-classical partition function in different ensembles and find that there exist two possible thermodynamic schemes, with different outcomes. Regarding the traditional scheme (scheme I), where the length cutoff is identified with the AdS radius, we show that charged BTZ-like black holes are super-entropic, namely they violate the reverse isoperimetric inequality conjecture, and their super-entropicity is strongly connected to a fundamental thermodynamic instability. This class of solutions is the first demonstration of super-entropic black holes which possess second-order critical points and, since thermodynamic instabilities always arise, it is not possible to physically interpret the corresponding van der Waals critical phenomenon in this scheme. In the second scheme (II) where the length cutoff is considered as an independent variable, namely the system respects the conjectured reverse isoperimetric inequality, we show that the solutions are thermodynamically stable in an ensemble where the length cutoff is kept fixed, and hence one can provide an explanation for the van der Waals critical phenomenon. Furthermore, in order to verify the consistency of the second scheme, we study the Joule-Thomson expansion and we extract the Joule-Thomson coefficient, the inversion temperature, the inversion curves, and the isenthalpic curves. The results indicate that this class of AdS black holes can be considered as interacting statistical systems. Additionally, in the D -> 3 limit we recover the conventional charge BTZ black holes, as well as their thermodynamic properties. Finally, we report a new thermodynamic instability for charged BTZ black holes, as well as their generalization to higher dimensions, which implies that working in an ensemble with fixed length cutoff is mandatory to consistently examine the thermodynamic processes.