{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T13:06:21Z","timestamp":1789391181712,"version":"build-2803163510"},"reference-count":42,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T00:00:00Z","timestamp":1789344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Higher Education and Science Committee of the Ministry of Education, Science, Culture and Sports (MESCS) of the Republic of Armenia","award":["21AG-4C075"],"award-info":[{"award-number":["21AG-4C075"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Finite-time heat engines must balance useful power output against irreversibility. We develop a decision-theoretic framework for ecological optimization of the endoreversible Curzon\u2013Ahlborn engine based on its normalized power\u2013loss Pareto frontier. We first examine bargaining-based selection rules. For Newtonian heat transfer, a symmetric Nash compromise between retained power and reduced exergy destruction selects a unique interior operating point with efficiency \u03b7N=1\u2212\u03c43\/4, where \u03c4=Tc\/Th is the cold-to-hot reservoir temperature ratio. The same Newtonian state is recovered by the Arias-Hern\u00e1ndez\u2013Angulo-Brown prescription, which fixes the ecological weight from the maximum-power reference. Our contribution is therefore not a new efficiency law but a decision-theoretic interpretation of the established 3\/4 law as a distinguished compromise between maximum-power operation and the reversible Carnot limit. Under the same normalization, the Kalai\u2013Smorodinsky and egalitarian selectors also identify the same balance point. We then extend the bargaining analysis beyond Newton\u2019s law of cooling and compare the Nash continuation with the Arias-Hern\u00e1ndez\u2013Angulo-Brown E\u03f5 \u2212 C\u03f5 prescription. Although coinciding in the Newtonian limit, the two approaches separate at first order when the heat-transfer law is perturbed, thereby distinguishing their underlying selection principles. This comparison raises a further question: how should an operating state be chosen when the relative priority assigned to power and irreversibility reduction is itself uncertain? We address this question through minimax-regret optimization, which selects the operating point that minimizes the largest loss relative to the optimum that would have been chosen had the priority been known. Under complete normalized uncertainty in the ecological priority, the regret-robust selector again yields \u03b7=1\u2212\u03c43\/4, giving the same operating state a complementary interpretation in terms of robustness to priority uncertainty.<\/jats:p>","DOI":"10.3390\/e28091023","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T12:09:51Z","timestamp":1789387791000},"page":"1023","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Decision-Theoretic Ecological Optimization of the Curzon\u2013Ahlborn Heat Engine"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2194-0192","authenticated-orcid":false,"given":"Karen K.","family":"Huruntz","sequence":"first","affiliation":[{"name":"Department of Biology, Yerevan State University, Yerevan 0025, Armenia"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Lilit E.","family":"Ghukasyan","sequence":"additional","affiliation":[{"name":"Department of Biology, Yerevan State University, Yerevan 0025, Armenia"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5649-0067","authenticated-orcid":false,"given":"Ashok","family":"Vaseashta","sequence":"additional","affiliation":[{"name":"Strategic Research, International Clean Water Institute, Manassas, VA 20108-0258, USA"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"conceptualization","vocabulary":"credit"}]},{"given":"Artak V.","family":"Gevorgyan","sequence":"additional","affiliation":[{"name":"Institute of Mechanics, Yerevan 0019, Armenia"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2086","DOI":"10.1103\/PhysRevA.15.2086","article-title":"Thermodynamics in finite time. 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