To the development of statistical thermodynamics and technique оf fractal analysis for non-extensive systems based on entropy and discrimination information of Renyi

The article shows how one can obtain statistical thermodynamics of nonextensive systems and determine its properties on the basis of parametric entropy and discrimination information of Renyi. This exploration is based on not Gibbsian equilibrium distribution obtained from the extremum condition Renyi entropy, while preservation an average energy of the system, as well as on the averaging of its of random parameters over an escort (normalized) distribution, convenient when considering the chaotic, fractal and multifractal systems. It is shown that in the microcanonical ensemble the Renyi statistic is equivalent to Boltzmann–Gibbs statistics. It is found that the temporal evolution of a closed stochastic system to the equilibrium state depends on the sign of the parameter $q$, which is a measure of the nonextensivity of Renyi statistics. Discusses different ways of constructing measures different orders of multifractales on the basis of entropy and discrimination information of Renyi and analyzed their specifics.