{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:26:37Z","timestamp":1760235997335,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,14]],"date-time":"2021-10-14T00:00:00Z","timestamp":1634169600000},"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>Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. The first aim of this paper is to introduce and study the economic Carnot cycles concerning Roegenian economics, using our thermodynamic\u2013economic dictionary. These cycles are described in both a Q\u2212P diagram and a E\u2212I diagram. An economic Carnot cycle has a maximum efficiency for a reversible economic \u201cengine\u201d. Three problems together with their solutions clarify the meaning of the economic Carnot cycle, in our context. Then we transform the ideal gas theory into the ideal income theory. The second aim is to analyze the economic Van der Waals equation, showing that the diffeomorphic-invariant information about the Van der Waals surface can be obtained by examining a cuspidal potential.<\/jats:p>","DOI":"10.3390\/e23101344","type":"journal-article","created":{"date-parts":[[2021,10,14]],"date-time":"2021-10-14T22:42:18Z","timestamp":1634251338000},"page":"1344","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Economic Cycles of Carnot Type"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7132-6900","authenticated-orcid":false,"given":"Constantin","family":"Udriste","sequence":"first","affiliation":[{"name":"Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, 060042 Bucharest, Romania"},{"name":"Academy of Romanian Scientists, Ilfov 3, Sector 5, 050044 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9758-3833","authenticated-orcid":false,"given":"Vladimir","family":"Golubyatnikov","sequence":"additional","affiliation":[{"name":"Department of Inverse and Ill-Posed Problems, Sobolev Institute of Mathematics SB RAS, Kotpyug Avenue 4, 630090 Novosibirsk, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9160-9185","authenticated-orcid":false,"given":"Ionel","family":"Tevy","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, 060042 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,14]]},"reference":[{"key":"ref_1","unstructured":"Udriste, C., Ferrara, M., and Opris, D. 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