to be well understood. In the past 40 years, after the foundations of the standard thermodynamic theory of black holes [@Bekenstein:1973ur; @Bardeen:1973gs; @Hawking:1974sw; @Hawking:1976de], numerous achievements have been made in the field. In spite of the active research and successes however, there still are some unsettled and important issues which could not be resolved satisfactorily so far. From a classical thermodynamic perspective, one of the most interesting ones is the nonextensive nature of black holes and the corresponding problem of thermodynamic stability.

A basic group of physical quantities in classical thermodynamics is the group called extensive variables $X$ (like energy, entropy, etc.), where it is assumed that these quantities are *additive* for composition, i.e. $X_{12}=X_1+X_2$ when thermodynamic systems are joined together [@PhysRevE.83.061147]. On the other hand, it is also customary to assume that these quantities characterize the system down to the smallest scales [@Mackey], i.e. when working with finite densities: $$\varrho_X = \lim_{n\rightarrow\infty}\frac{1}{n}\sum_{i=1}^n X_i < \infty,$$ where the system is divided into $n$ different parts. This property is called *extensivity*. The two properties: additivity and extensivity are not equivalent. An additive quantity is extensive, but extensive quantities can be nonadditive too [@T2; @B1]. Black holes are very peculiar creatures in 