Thermodynamic Topology and Phase Space Analysis of AdS Black Holes Through Non-Extensive Entropy Perspectives
Saeed Noori Gashti, Behnam Pourhassan, Izzet Sakalli
TL;DR
This work investigates the thermodynamic topology of AdS Einstein-power-Yang-Mills black holes under non-extensive entropies within bulk-boundary and restricted phase space frameworks. By employing Duan's phi-mapping and a generalized free energy, the authors classify black-hole solutions through topological charges $\omega$ and track how these charges depend on non-extensive parameters ($\delta, \lambda, \alpha, \beta, K, \Delta$). Across entropies, bulk-boundary results show rich, parameter-dependent topological patterns, while in RPS the topology tends to stabilize, yielding a universal $\omega = +1$ for Rényi, Sharma-Mittal and Tsallis-Cirto (with Barrow and Kaniadakis exhibiting parameter-driven transitions). These findings offer a topological lens on entropy generalizations in holographic black-hole thermodynamics and hint at broader implications for stability analyses and non-extensive thermodynamics in gravitational systems.
Abstract
This paper studies the thermodynamic topology through the bulk-boundary and restricted phase space (RPS) frameworks. In bulk-boundary framework, we observe two topological charges $(ω= +1, -1)$ concerning the non-extensive Barrow parameter and with ($δ=0$) in Bekenstein-Hawking entropy. For Renyi entropy, different topological charges are observed depending on the value of the $λ$ with a notable transition from three topological charges $(ω= +1, -1, +1)$ to a single topological charge $(ω= +1)$ as $λ$ increases. Also, by setting $λ$ to zero results in two topological charges $(ω= +1, -1)$. Sharma-Mittal entropy exhibits three distinct ranges of topological charges influenced by the $α$ and $β$ with different classifications viz $β$ exceeds $α$, we will have $(ω= +1, -1, +1)$, $β= α$, we have $(ω= +1, -1)$ and for $α$ exceeds $β$ we face $(ω= -1)$. Also, Kaniadakis entropy shows variations in topological charges viz we observe $(ω= +1, -1)$ for any acceptable value of $K$, except when $K = 0$, where a single topological charge $(ω= -1)$. In the case of Tsallis-Cirto entropy, for small parameter $Δ$ values, we have $(ω= +1)$ and when $Δ$ increases to 0.9, we will have $(ω= +1, -1)$. When we extend our analysis to the RPS framework, we find that the topological charge consistently remains $(ω= +1)$ independent of the specific values of the free parameters for Renyi, Sharma-Mittal, and Tsallis-Cirto. Additionally, for Barrow entropy in RPS, the number of topological charges rises when $δ$ increases from 0 to 0.8. Finally for Kaniadakis entropy, at small values of $K$, we observe $(ω= +1)$. However, as the non-extensive parameter $K$ increases, we encounter different topological charges and classifications with $(ω= +1, -1)$.