{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T12:48:06Z","timestamp":1768567686019,"version":"3.49.0"},"reference-count":53,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,23]],"date-time":"2019-07-23T00:00:00Z","timestamp":1563840000000},"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>We study the minimally nonlinear irreversible heat engines in which the time-reversal symmetry for the systems may be broken. The expressions for the power and the efficiency are derived, in which the effects of the nonlinear terms due to dissipations are included. We show that, as within the linear responses, the minimally nonlinear irreversible heat engines can enable attainment of Carnot efficiency at positive power. We also find that the Curzon-Ahlborn limit imposed on the efficiency at maximum power can be overcome if the time-reversal symmetry is broken.<\/jats:p>","DOI":"10.3390\/e21070717","type":"journal-article","created":{"date-parts":[[2019,7,23]],"date-time":"2019-07-23T10:44:51Z","timestamp":1563878691000},"page":"717","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Efficiency Bounds for Minimally Nonlinear Irreversible Heat Engines with Broken Time-Reversal Symmetry"],"prefix":"10.3390","volume":"21","author":[{"given":"Qin","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Physics, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Physics, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Physics, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jizhou","family":"He","sequence":"additional","affiliation":[{"name":"Department of Physics, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianhui","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Physics, Nanchang University, Nanchang 330031, China"},{"name":"State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China"},{"name":"State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,23]]},"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":"43","author":"Curzon","year":"1975","journal-title":"Am. 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