标题： 非广延熵框架下全息热力学的拓扑结构 显示英文标题

标题： Topology of Holographic Thermodynamics within Non-extensive Entropy

摘要： 本文中，我们通过采用非广延熵框架研究了AdS Reissner-Nordstr$\ddot{o}$m (R-N) 黑洞的热力学拓扑结构，具体使用了R$\acute{e}$nyi熵（具有非广延参数$\lambda$）和Sharma-Mittal熵（具有非广延参数$\alpha, \beta$）。我们的研究涵盖了两种框架：体-边界热力学和受限相空间（RPS）热力学。 在体-边界框架下，我们遇到了奇异零点，揭示了由自由参数$(\lambda)$影响的拓扑荷，其中正拓扑荷为$(\omega = +1)$，总拓扑荷为$(W = +1)$，表明存在一个单一稳定的定域黑洞。 进一步分析表明，当将$(\lambda)$设置为零时，方程与贝肯斯坦-霍金熵结构对齐，并表现出与多种拓扑电荷$(\omega = +1, -1, +1)$不同的行为。 值得注意的是，在 Sharma-Mittal 熵中增加参数$\alpha$会导致具有总拓扑电荷$(W = +1)$的多种拓扑电荷$(\omega = +1, -1, +1)$。 相反，增加$(\beta)$会减少拓扑电荷的数量，同时保持总拓扑电荷$(W = +1)$。 将我们的研究扩展到受限相空间时，在所有条件和参数下都观察到了一致的拓扑荷$(\omega = +1)$。 即使退化为贝肯斯坦-霍金熵时，这种一致性仍然存在，这表明在受限相空间（RPS）中的非延展态和霍金熵态表现出相似的行为。 显示英文摘要

摘要： In this paper, we delve into the thermodynamic topology of AdS Reissner-Nordstr$\ddot{o}$m (R-N) black holes by employing nonextensive entropy frameworks, specifically R$\acute{e}$nyi (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 $(\omega = +1)$ and the total topological charge $(W = +1)$, 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 $(\omega = +1, -1, +1)$. Notably, increasing the parameter $\alpha$ in Sharma-Mittal entropy results in multiple topological charges $(\omega = +1, -1, +1)$ with the total topological charge $(W = +1)$. Conversely, increasing $(\beta)$ reduces the number of topological charges, maintaining the total topological charge $(W = +1)$. Extending our study to the restricted phase space, we observe consistent topological charges $(\omega = +1)$ 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.