{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T12:32:27Z","timestamp":1775392347504,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,19]],"date-time":"2017-07-19T00:00:00Z","timestamp":1500422400000},"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>Finite Time Thermodynamics is generally associated with the Curzon\u2013Ahlborn approach to the Carnot cycle. Recently, previous publications on the subject were discovered, which prove that the history of Finite Time Thermodynamics started more than sixty years before even the work of Chambadal and Novikov (1957). The paper proposes a careful examination of the similarities and differences between these pioneering works and the consequences they had on the works that followed. The modelling of the Carnot engine was carried out in three steps, namely (1) modelling with time durations of the isothermal processes, as done by Curzon and Ahlborn; (2) modelling at a steady-state operation regime for which the time does not appear explicitly; and (3) modelling of transient conditions which requires the time to appear explicitly. Whatever the method of modelling used, the subsequent optimization appears to be related to specific physical dimensions. The main goal of the methodology is to choose the objective function, which here is the power, and to define the associated constraints. We propose a specific approach, focusing on the main functions that respond to engineering requirements. The study of the Carnot engine illustrates the synthesis carried out and proves that the primary interest for an engineer is mainly connected to what we called Finite (physical) Dimensions Optimal Thermodynamics, including time in the case of transient modelling.<\/jats:p>","DOI":"10.3390\/e19070369","type":"journal-article","created":{"date-parts":[[2017,7,20]],"date-time":"2017-07-20T04:28:26Z","timestamp":1500524906000},"page":"369","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["The History and Perspectives of Efficiency at Maximum Power of the Carnot Engine"],"prefix":"10.3390","volume":"19","author":[{"given":"Michel","family":"Feidt","sequence":"first","affiliation":[{"name":"Laboratoire d\u2019\u00c9nerg\u00e9tique et de M\u00e9canique Th\u00e9orique et Appliqu\u00e9e, UMR 7563, Universit\u00e9 de Lorraine, 54518 Vandoeuvre-l\u00e8s-Nancy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1119\/1.10023","article-title":"Efficiency of a Carnot Engine at Maximum Power Output","volume":"1","author":"Curzon","year":"1975","journal-title":"Am. J. Phys."},{"key":"ref_2","unstructured":"Chambadal, P. (1957). Les Centrales Nucl\u00e9aires, A. Colin. (In French)."},{"key":"ref_3","first-page":"125","article-title":"The efficiency of atomic power stations (a review)","volume":"7","author":"Novikov","year":"1958","journal-title":"J. Nucl. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1515\/jnet-2014-0018","article-title":"Reitlinger and the origins of the efficiency at maximum power formula for heat engines","volume":"39","author":"Vaudrey","year":"2014","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_5","unstructured":"Chisacof, A., Petrescu, S., Costea, M., and Borcila, B. (2016, January 29\u201330). The History of \u201cNice Radical\u201d and its Importance in Optimizing the Mechanical Work or Power Output of Reversible and Irreversible Cycles. Proceedings of the Colloque Francophone sur l\u2019Energie, Environnement, Economie et Thermodynamique\u2014COFRET\u201916, Bucharest, Romania."},{"key":"ref_6","unstructured":"Moutier, J. (1872). \u00c9l\u00e9ments de Thermodynamique, Gautier-Villars. (In French)."},{"key":"ref_7","unstructured":"Danel, q. (2016). Etude Num\u00e9rique et Exp\u00e9rimentale d\u2019un Cycle de Rankine\u2014Hirn de Faible Puissance Pour lar\u00e9cup\u00e9ration D\u2019\u00e9nergie. [Ph.D. Thesis, Conservatoire National des Arts et M\u00e9tiers]. (In French)."},{"key":"ref_8","unstructured":"Rey, J. (1928). De l\u2019utilisation de l\u2019\u00e9nergie des eaux chaudes industrielles et naturelles. Chaleur et Industrie, 217\u2013226. (In French)."},{"key":"ref_9","unstructured":"Serrier, L. (1888). Trait\u00e9 de Physique Industrielle: Production et Utilisation de la Chaleur (Machines \u00e0 air Chaud), G. Masson. (In French)."},{"key":"ref_10","unstructured":"Petrescu, S., Costea, M., Feidt, M., Ganea, I., and Boriaru, N. (2015). Advanced Thermodynamics of Irreversible Processes with Finite Speed and Finite Dimensions. A Historical and Epistemological Approach, with Extension to Biological and Social Systems, AGIR Publishing House."},{"key":"ref_11","first-page":"809","article-title":"The maximum power efficiency 1\u2212\u221a\u03c4: Research, education and bibliometric relevance","volume":"224","author":"Roco","year":"2015","journal-title":"Eur. Phys. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1016\/j.applthermaleng.2006.09.020","article-title":"Optimization of Direct Carnot Cycle","volume":"27","author":"Feidt","year":"2007","journal-title":"Appl. Therm. 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Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/7\/369\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:16Z","timestamp":1760208196000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/7\/369"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,19]]},"references-count":19,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2017,7]]}},"alternative-id":["e19070369"],"URL":"https:\/\/doi.org\/10.3390\/e19070369","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,19]]}}}