We investigate the gravitational origin of the Tsallis entropy, characterized by the nonadditive index δ. Utilizing Wald's formalism within the framework of f(R) modified theories of gravity, we evaluate the entropy on the black hole horizon for constant curvature solutions to the spherically symmetric vacuum field equations. In so doing, we demonstrate that the Tsallis entropy can be effectively derived from a generalization of the Lagrangian L∝R1+ϵ, where ϵ=δ−1 quantifies small deviations from general relativity. In conclusion, we examine the physical implications of our findings in light of cosmological observations and elaborate on the possibility of solving the thermodynamic instability of Schwarzschild black holes.

中文翻译：

---

Tsallis 熵的拉格朗日公式


我们研究了 Tsallis 熵的引力起源，其特征是非加性指数 δ。利用 f(R) 修正引力理论框架内的 Wald 形式主义，我们评估了球对称真空场方程常曲率解的黑洞视界上的熵。通过这样做，我们证明了 Tsallis 熵可以有效地从拉格朗日 L∝R1+ϵ 的推广中导出，其中 ϵ=δ−1 量化了与广义相对论的小偏差。总之，我们根据宇宙学观测研究了我们的发现的物理含义，并详细阐述了解决史瓦西黑洞热力学不稳定性的可能性。