Elements of Formalism of Curado–Tsallis Nonadditive Statistics. Rathie–Kannappan Difference Information

Abstract

A logical scheme of presentation of principles of nonadditive (nonextensive) statistics and thermodynamics has been given, based on parametric definition of Tsallis entropy. The principle of maximum entropy was used to find probability equilibrium \(q\)-distributions, which at large deviations of a random variable from the mean value have power asymptotics corresponding to empirically established regularities for a wide class of objects to which classical statistical mechanics is not applicable. Consequences of non-normalized Curado–Tsallis averaging of microscopic physical quantities in Tsallis statistics and its formal and practical significance for modeling dynamic \(q\)-systems, which has recently been presented in large quantities in the literature, have been analyzed. Based on Rathie–Kannappan difference information, spontaneous transitions between system states and a generalized H-theorem have been considered.