This article is cited in 2 papers

Two-parameter entropy the Sharma–Mittal functional as core family of nonlinear Fokker–Planck–Kolmogorov equations

A. V. Kolesnichenko


Abstract: An important aspect related to the derivation of nonlinear power-law equations of Fokker–Planck–Kolmogorov correlated with the Sharma–Mittal entropy is analyzed in this work. In this case, the obtained diffusion equations are written in such a way that their stationary solutions are probability distributions that maximize the ShM entropy for non-extensive systems. The ansatz approach is used to obtain exact solutions of nonlinear nonstationary one-dimensional FPK equations associated with the Tsallis, Renyi, and Sharma–Mittal entropies.

Keywords: principles of nonextensive statistical mechanics, Sharma–Mittal entropy, power law of distribution.

DOI: 10.20948/prepr-2021-3