Two-parameter functional of entropy Sharma-Mittal as the basis of the family of generalized thermodynamices of non-extensive systems
Abstract:
The properties of the family of generalized entropies given by the Sharm−Mittal entropy, which includes the entropy of Tsallis, the Renyi entropy, the Landsberg−Vedral entropy, the Gauss entropy, and the classical Boltzmann−Gibbs−Shannon entropy are investigated. Based on the Sharm-Mittal statistics, the two-parameter thermodynamics of non-extensive systems is constructed and its interrelation with generalized one-parameter thermodynamices based on the named deformed entropies of the family is shown. A generalization of the zero law of thermodynamics is obtained for two independent non-extensive systems at their thermal contact, introduce into consideration a so-called physical temperature different from the inversion of the Lagrange multiplier β. Taking into account the generalized first law of thermodynamics and the Legendre transformation, a redefinition of the thermodynamic relationships obtained within the framework of the Sharma Mittal statistics is given. On the basis of the two-parametric information of Sharm-Mittal's difference, Gibbs's theorem and the H-theorem on the change of these measures in the course of time evolution are formulated and proved.
Keywords:
principles of nonextensive statistical mechanics, Sharma-Mittal entropy, power law of distribution
Publication language:russian, pages:35
Research direction:
Mathematical modelling in actual problems of science and technics
