Key points are not available for this paper at this time.
Abstract In this paper, we study the thermodynamic topology of AdS Einstein–power–Yang–Mills black holes, examining them through both the bulk-boundary and restricted phase space (RPS) frameworks. We consider various non-extensive entropy models, including Barrow (δ), Rényi (λ), Sharma–Mittal (β, α), Kaniadakis (K), and Tsallis-Cirto entropy (Δ). Initially, we analyze the thermodynamic topology within the bulk-boundary framework. Our findings highlight the influence of free parameters on topological charges. We observe two topological charges (= +1, -1) (ω = + 1, - 1) with respect to the non-extensive Barrow parameter and also with (=0 δ = 0) in Bekenstein–Hawking entropy. For Rényi entropy, different topological charges are observed depending on the value of the λ with a notable transition from three topological charges (= +1, -1, +1) (ω = + 1, - 1, + 1) to a single topological charge (= +1) (ω = + 1) as λ increases. Also, by setting λ to zero results in two topological charges (= +1, -1) (ω = + 1, - 1). Sharma–Mittal entropy exhibits three distinct ranges of topological charges influenced by the α and β with different classifications viz, if β exceeds α, we will have (= +1, -1, +1) (ω = + 1, - 1, + 1) ; if = β = α, we have (= +1, -1) (ω = +
Gashti et al. (Sun,) studied this question.