{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T19:21:27Z","timestamp":1762543287638,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,8,13]],"date-time":"2020-08-13T00:00:00Z","timestamp":1597276800000},"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 paper, we consider optimal trading processes in economic systems. The analysis is based on accounting for irreversibility factors using the wealth function concept. The existence of the welfare function is proved, the concept of capital dissipation is introduced as a measure of the irreversibility of processes in the microeconomic system, and the economic balances are recorded, including capital dissipation. Problems in the form of kinetic equations leading to given conditions of minimal dissipation are considered.<\/jats:p>","DOI":"10.3390\/e22080891","type":"journal-article","created":{"date-parts":[[2020,8,13]],"date-time":"2020-08-13T09:23:44Z","timestamp":1597310624000},"page":"891","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Finite-Time Thermodynamics in Economics"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3637-6160","authenticated-orcid":false,"given":"Anatoly","family":"Tsirlin","sequence":"first","affiliation":[{"name":"Ailamazyan Program Systems Institute of Russian Academy of Sciences, 152120 Rostov, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2371-9045","authenticated-orcid":false,"given":"Larisa","family":"Gagarina","sequence":"additional","affiliation":[{"name":"Institute of Systems and Program Engineering and Information Technologies, National Research University of Electronic Technology, 124482 Zelenograd, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,13]]},"reference":[{"key":"ref_1","unstructured":"Petrov, A.A. 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Foundations of Economic Analysis, Harvard University Press."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/8\/891\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:00:24Z","timestamp":1760176824000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/8\/891"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,13]]},"references-count":11,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["e22080891"],"URL":"https:\/\/doi.org\/10.3390\/e22080891","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,8,13]]}}}