@Oppenheim:2002kx; @Pesci:2006sb; @Aranha:2008ni; @Tsallis:2012js] and references therein). The general theory of nonadditive thermodynamics has also advanced significantly in the past few decades (see e.g. [@T2; @Landsberg] and references therein), and it has been shown, that by relaxing the additivity requirement in the axiomatic approach to the entropy definition (given by Shannon [@Shannon] and Khinchin [@Khinchin]) to the weaker *composability* requirement, new possible functional forms of the entropy may arise [@Tempesta]. As a consequence, there exist certain parametric extensions of the Boltzamann–Gibbs statistical entropy formula, which seem to be more appropriate to describe systems with long-range type interactions. One such statistical entropy definition has been proposed by Tsallis [@Tsallis:1987eu] as: $$\label{TsS}
 S_T=\frac{1}{1-q}\sum_i(p^q_i-p_i),$$ where $p_i$ are the probabilities of the microscopic states of the system, and $q\in\mathbb{R}$ is the so-called nonextensivity parameter. In the limit of $q\rightarrow 1$, $S_T$ reproduces the standard Boltzamann–Gibbs result, however, in the case when $q\neq 0$, the Tsallis entropy is not additive, and the parameter can be attributed to measure the effects of non-localities in the system. The $q$-parameter is usually constant in different physical situations, and its explicit value is part of the problem to be solved.

The Tsallis statistics to the black hole problem has 