black hole entropy problem [@Biro:2013cra]. In this model, in order to satisfy both the equilibrium the zeroth law compatibility, instead of the Tsallis description, we considered its formal logarithm, the Rényi statistics (\[TsS\]) to describe the thermodynamic entropy of black hole event horizons. The explicit details of this approach is presented in the next section, and by applying the Rényi model to Schwarzschild black holes [@Biro:2013cra], we found that the temperature-horizon radius relation of the black hole has the same form as the one obtained from a black hole in anti-de Sitter space by using the original Boltzamann-Gibbs statistics. In both cases the temperature has a minimum. By using a semi-classical estimate on the horizon radius at this minimum, we obtained a Bekenstein bound [@Bekenstein:1980jp] for the $q$-parameter value in the Rényi entropy of micro black holes ($q \geq 1 + 2/\pi^2$), which was surprisingly close to other $q$-parameter fits from very distant and unrelated physical phenomena, e.g. cosmic ray spectra [@Bek1; @Bek2], and power-law distribution of quarks coalescing to hadrons in high energy accelerator experiments [@BU].

Besides the statistical approach, another fundamental problem of applying standard thermodynamic methods to black holes arising from the question of stability. In ordinary 