Researchers have explored the thermodynamic topological classification of d-dimensional Reissner-Nordström (RN) black holes confined within a cavity and with fixed charge. Using the reduced Euclidean action, they constructed an off-shell vector field from the quasilocal energy, entropy, and on-shell inverse temperature. This approach has allowed them to assign topological classes to these black holes, a method that offers a new perspective on their thermodynamic properties.

The study reveals that the presence of a finite cavity induces two charge-dependent topological classes. Neutral black holes are classified as $W^{0-}$, while charged black holes belong to $W^{1+}$. Interestingly, by extending the cavity radius to infinity, while keeping the physical charge constant, the endpoint data changes. In this scenario, neutral black holes become $W^{1-}$ and charged ones become $W^{0+}$.

These results suggest that the electric charge and the outer boundary of the cavity are the determining factors in the refined topological classification of this family of RN black holes, beyond the spacetime dimension, as observed in explicit four- and five-dimensional examples. This finding underscores the importance of the environment in characterizing the fundamental properties of black holes.