Some properties of the Sharma–Mittal statistical distribution

Abstract

The statistical theory based on the two-parameter Sharma–Mittal functional is a generalization of the statistics of Gibbs, Renyi and Tsallis. In this paper, the formalism of statistical mechanics based on the Sharma–Mittal entropy functional is considered, and the theorem on the equidistribution of energy for classical statistical systems by degrees of freedom is proved. A generalized Maxwell distribution for the corresponding statistics is obtained and the characteristics of statistical systems described by the distribution are calculated: the average velocity modulus, the root-mean-square and the most probable velocities of gas particles. A generalized Sakura–Tetrode formula is also obtained.