been investigated with various approaches (see e.g. [@Tsallis:2012js] and references therein), however it has been a long-standing problem in nonextensive thermodynamics that nonadditive entropy composition rules (in general) can not be compatible with the most natural requirement of thermal equilibrium in the system [@PhysRevE.83.061147]. They usually don’t satisfy the zeroth law of thermodynamics, which requires the existence of a well defined, unique, empirical temperature in thermal equilibrium which is constant all over the system. For resolving these issues, Biró and Ván developed a method [@PhysRevE.83.061147], called the “*formal logarithm approach*”, which maps the original, nonadditive entropy composition rule of a given system to an additive one by a simple transformation. This procedure results a new, but also well defined entropy function for the system, which in turn, also satisfies both the equilibrium and the zeroth law compatibility requirements of thermodynamics. In case of the nonextensive Tsallis statistics, this new entropy turns out to be the well known Rényi formula [@renyi1959dimension; @renyi1970probability], defined as $$\label{Srenyi}
S_R=\frac{1}{1-q}\ln\sum_ip^q_i,$$ which had been proposed earlier by the Hungarian mathematician Alfréd Rényi in 1959 [@renyi1959dimension].

Recently, motivated by the nonextensive and nonlocal nature of black hole thermodynamics, we proposed and studied an alternative approach to the 