Abstract We study the thermodynamic topology of charged anti-de Sitter (AdS) black holes with non-extensive entropy corrections within an entropy–geometry correspondence framework and its holographic realization. By reconstructing the bulk geometry from modified entropy functionals, we analyze the phase structure using the off-shell free energy and define a thermodynamic vector field whose zeros characterize equilibrium states. The associated winding numbers provide a topological classification of black hole phases. Extending the analysis to the dual boundary theory, we establish an exact matching between bulk and boundary topological charges. This demonstrates that thermodynamic topology is preserved under holographic duality and provides a universal framework for characterizing entropy-deformed black hole phase transitions.
Anand et al. (Wed,) studied this question.