{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T10:50:25Z","timestamp":1779101425942,"version":"3.51.4"},"reference-count":25,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T00:00:00Z","timestamp":1750118400000},"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":"<jats:p>In this manuscript, the typical problems of \u201cfinite-time thermodynamics\u201d, their general methodology, and the general features of their solutions are considered. We also consider the role of minimal dissipation processes, the properties of the irreversibility index, and the consequences of its existence. A generalization of the Carath\u00e9odory theorem for averaged optimization problems corresponding to cyclic processes and the properties of optimal solutions following from it are given. The existence of the irreversibility index for economic macrosystems and their analogies to and differences from thermodynamic systems are proven.<\/jats:p>","DOI":"10.3390\/e27060649","type":"journal-article","created":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T11:53:14Z","timestamp":1750161194000},"page":"649","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Finite-Time Thermodynamics: Problems, Approaches, and Results"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3637-6160","authenticated-orcid":false,"given":"Anatoly M.","family":"Tsirlin","sequence":"first","affiliation":[{"name":"System Analysis Research Center, Ailamazyan Program Systems Institute of RAS, 152021 Pereslavl-Zalessky, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3068-9956","authenticated-orcid":false,"given":"Alexander I.","family":"Balunov","sequence":"additional","affiliation":[{"name":"System Analysis Research Center, Ailamazyan Program Systems Institute of RAS, 152021 Pereslavl-Zalessky, Russia"},{"name":"Department of Cybernetics, Yaroslavl State Technical University, 150023 Yaroslavl, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9861-5796","authenticated-orcid":false,"given":"Ivan A.","family":"Sukin","sequence":"additional","affiliation":[{"name":"System Analysis Research Center, Ailamazyan Program Systems Institute of RAS, 152021 Pereslavl-Zalessky, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,17]]},"reference":[{"key":"ref_1","first-page":"125","article-title":"The efficiency of atomic power stations","volume":"7","author":"Novikov","year":"1958","journal-title":"J. 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(In Russian)."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/6\/649\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:53:54Z","timestamp":1760032434000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/6\/649"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,17]]},"references-count":25,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["e27060649"],"URL":"https:\/\/doi.org\/10.3390\/e27060649","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,17]]}}}