{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:21:12Z","timestamp":1773656472954,"version":"3.50.1"},"reference-count":0,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2008,12,8]],"date-time":"2008-12-08T00:00:00Z","timestamp":1228694400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The speed-gradient variational principle (SG-principle) for nonstationary far from equilibrium systems is formulated and illustrated by examples. The SG-model of transient (relaxation) dynamics for systems of a finite number of particles based on maximum entropy principle is derived. It has the form dX(t)\/dt = AlnX(t); where X(t) is the vector of the cell populations, A is a symmetric matrix with two zero eigenvalues corresponding to mass and energy conservation laws.<\/jats:p>","DOI":"10.3390\/e10040757","type":"journal-article","created":{"date-parts":[[2008,12,8]],"date-time":"2008-12-08T05:44:25Z","timestamp":1228715065000},"page":"757-764","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Speed-gradient Entropy Principle for Nonstationary Processes"],"prefix":"10.3390","volume":"10","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"}]}],"member":"1968","published-online":{"date-parts":[[2008,12,8]]},"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/10\/4\/757\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:21:14Z","timestamp":1760221274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/10\/4\/757"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,12,8]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2008,12]]}},"alternative-id":["e10040757"],"URL":"https:\/\/doi.org\/10.3390\/e10040757","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,12,8]]}}}