{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,3]],"date-time":"2024-08-03T13:20:48Z","timestamp":1722691248743},"reference-count":25,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,3,6]],"date-time":"2015-03-06T00:00:00Z","timestamp":1425600000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"In this paper we consider dynamics of non-stationary processes that follow the MaxEnt principle. We derive a set of equations describing dynamics of a system for Shannon and Tsallis entropies. Systems with discrete probability distribution are considered under mass conservation and energy conservation constraints. The existence and uniqueness of solution are established and asymptotic stability of the equilibrium is proved. Equations are derived based on the speed-gradient principle originated in control theory.<\/jats:p>","DOI":"10.3390\/e17031090","type":"journal-article","created":{"date-parts":[[2015,3,6]],"date-time":"2015-03-06T15:38:33Z","timestamp":1425656313000},"page":"1090-1102","source":"Crossref","is-referenced-by-count":17,"title":["Speed Gradient and MaxEnt Principles for Shannon and Tsallis Entropies"],"prefix":"10.3390","volume":"17","author":[{"given":"Alexander","family":"Fradkov","sequence":"first","affiliation":[{"name":"Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, 61, Bolshoy ave. V.O., 199178 Saint-Petersburg, Russia"},{"name":"Mathematics and Mechanics Faculty, Saint-Petersburg State University, Universitetsky prospekt, 28, 198504 Saint-Petersburg, Russia"}]},{"given":"Dmitry","family":"Shalymov","sequence":"additional","affiliation":[{"name":"Mathematics and Mechanics Faculty, Saint-Petersburg State University, Universitetsky prospekt, 28, 198504 Saint-Petersburg, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible generalization of Boltzmann\u2013Gibbs statistics","volume":"52","author":"Tsallis","year":"1988","journal-title":"J. Stat. 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