Topology of Holographic Thermodynamics within Non-extensive Entropy

In this paper, we delve into the thermodynamic topology of AdS Reissner-Nordström (R-N) black holes by employing nonextensive entropy frameworks, specifically Rényi (with nonextensive parameter \lambda) and Sharma-Mittal entropy (with nonextensive parameter \alpha, \beta). Our investigation spans two frameworks: bulk boundary and restricted phase space (RPS) thermodynamics. In the bulk boundary framework, we face singular zero points revealing topological charges influenced by the free parameter (\lambda) with a positive topological charge (\omega = +۱) and the total topological charge (W = +۱), indicating the presence of a single stable on-shell black hole. Further analysis shows that when (\lambda) is set to zero, the equations align with the Bekenstein-Hawking entropy structure, demonstrating different behaviors with multiple topological charges (\omega = +۱, -۱, +۱). Notably, increasing the parameter \alpha in Sharma-Mittal entropy results in multiple topological charges (\omega = +۱, -۱, +۱) with the total topological charge (W = +۱). Conversely, increasing (\beta) reduces the number of topological charges, maintaining the total topological charge (W = +۱). Extending our study to the restricted phase space, we observe consistent topological charges (\omega = +۱) across all conditions and parameters. This consistency persists even when reducing to Bekenstein-Hawking entropy, suggesting similar behaviors in both non-extended and Hawking entropy states within RPS.

کلیدواژه ها:

Thermodynamic topology ، Nonextensive entropy ، bulk boundary ، Restricted phase space