In this work we have investigated the effects of the two highlighted non-Gaussian entropies which are the modified Rnyi entropy and the so-called incomplete statistics in the analysis of the thermodynamics of black holes (BHs). We have obtained the equipartition theorems and after that we obtained the heat capacities for both approaches. Depending on the values of both λ-parameter and M, the BH mass, relative to a modified Rnyi entropy and, depending on the values of the q-parameter and M, the incomplete entropy can determine if the BH has an unstable thermal equilibrium or not for each model.

中文翻译：

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关于修正 Rnyi 熵的性质和黑洞热力学中的不完全统计方法

在这项工作中，我们研究了两个突出的非高斯熵，即修正的 Rnyi 熵和黑洞热力学分析中所谓的不完全统计的影响。我们已经获得了均分定理，然后我们获得了两种方法的热容。根据λ参数和M的值，BH 质量，相对于修正的 Rnyi 熵，以及根据q参数和M的值，不完全熵可以确定 BH 是否具有不稳定的热平衡或不是每个型号。