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.
Document Type:
Preprint
Language: Russian
Citation:
A. V. Kolesnichenko, “Two-parameter entropy the Sharma–Mittal functional as core family of nonlinear Fokker–Planck–Kolmogorov equations”, Keldysh Institute preprints, 2021, 003, 35 pp.
\Bibitem{Kol21}
\by A.~V.~Kolesnichenko
\paper Two-parameter entropy the Sharma--Mittal functional as core family of nonlinear Fokker--Planck--Kolmogorov equations
\jour Keldysh Institute preprints
\yr 2021
\papernumber 003
\totalpages 35
\mathnet{http://mi.mathnet.ru/ipmp2921}
\crossref{https://doi.org/10.20948/prepr-2021-3}
Linking options:
https://www.mathnet.ru/eng/ipmp2921
https://www.mathnet.ru/eng/ipmp/y2021/p3
This publication is cited in the following 2 articles:
Yu. A. Antonov, V. I. Zakharov, N. A. Sukhareva, “Entropy Functionals and Information Difference of Satellite-Monitoring Time Series”, Cosmic Res, 61:6 (2023), 522
Yu. A. Antonov, V. I. Zakharov, N. A. Sukhareva, “Entropiinye funktsionaly i informatsiya razlichiya vremennykh ryadov sputnikovogo monitoringa”, Kosmicheskie issledovaniya, 61:6 (2023), 498
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