To the construction of non-additive thermodynamics of complex systems on the basis of the statistics of Kurado–Tsallis

The article presents a logical scheme for constructing non-extensive statistics and equilibrium thermodynamics, based on the parametric definition of the entropy of Tsallis. The consequences of the non-normalized averaging of the Kurado–Tsallis microscopic physical quantities in the Tsallis statistics are analyzed and its theoretical and practical significance in constructing non-additive thermodynamics of anomalous $q$-systems. Based on discrimination information of Rathie–Kannappan, spontaneous transitions between arbitrary states of a complex system and a generalized $H$-theorem in non-extensive statistics are considered.