While the Bekenstein–Hawking entropy is the unique notion of entropy that makes classical black hole thermodynamics consistent, alternative entropy notions (Rényi, Tsallis, and generalized constructs) abound in the literature. We explore conditions under which they are part of a consistent horizon thermodynamics for certain classes of modified gravity black holes. We provide examples in which black hole masses and temperatures going hand-in-hand with these alternative entropies coincide with their usual counterparts associated with the Bekenstein–Hawking entropy.

中文翻译：

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替代熵和一致的黑洞热力学

虽然 Bekenstein-Hawking 熵是使经典黑洞热力学一致的熵的独特概念，但文献中有很多替代熵概念（Rényi、Tsallis 和广义构造）。我们探索了在何种条件下它们是某些类型的修正引力黑洞的一致视界热力学的一部分。我们提供了一些例子，其中黑洞质量和温度与这些替代熵密切相关，与它们通常与贝肯斯坦-霍金熵相关的对应物一致。