To the construction of the thermodynamics of non-additive media on the basis of the statistics of Tsallis–Mendes–Plastino

The consequences escort of averaging of Tsallis–Mendes–Plastino (TMP) of microscopic dynamic quantities in non-additive statistics of Tsallis and its formal and practical value in modeling various $q$-systems are analyzed. It is shown that, depending on the method for determining the average values of dynamic quantities, various versions of generalized equilibrium thermodynamics are possible and their comparative analysis is given. Conditions are found for performing the Legendre transformation using the concept of physical temperature. The modified thermodynamic relationships in the TMP statistics are considered. The method of optimized Lagrange multipliers is discussed, which allows eliminating some problems of TMP statistics.