{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T01:56:46Z","timestamp":1781056606504,"version":"3.54.1"},"reference-count":48,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,7]],"date-time":"2024-06-07T00:00:00Z","timestamp":1717718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NCCR SwissMAP"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Entanglement engines are autonomous quantum thermal machines designed to generate entanglement from the presence of a particle current flowing through the device. In this work, we investigate the functioning of a two-qubit entanglement engine beyond the steady-state regime. Within a master equation approach, we derive the time-dependent state, the particle current, as well as the associated current correlation functions. Our findings establish a direct connection between coherence and internal current, elucidating the existence of a critical current that serves as an indicator for entanglement in the steady state. We then apply our results to investigate kinetic uncertainty relations (KURs) at finite times. We demonstrate that there is more than one possible definition for KURs at finite times. Although the two definitions agree in the steady-state regime, they lead to different parameter ranges for violating KUR at finite times.<\/jats:p>","DOI":"10.3390\/e26060497","type":"journal-article","created":{"date-parts":[[2024,6,7]],"date-time":"2024-06-07T08:05:17Z","timestamp":1717747517000},"page":"497","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Finite-Time Dynamics of an Entanglement Engine: Current, Fluctuations and Kinetic Uncertainty Relations"],"prefix":"10.3390","volume":"26","author":[{"given":"Jeanne","family":"Bourgeois","sequence":"first","affiliation":[{"name":"Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gianmichele","family":"Blasi","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3366-624X","authenticated-orcid":false,"given":"Shishir","family":"Khandelwal","sequence":"additional","affiliation":[{"name":"Physics Department, Lund University, Box 118, 22100 Lund, Sweden"},{"name":"NanoLund, Lund University, Box 118, 22100 Lund, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7893-0177","authenticated-orcid":false,"given":"G\u00e9raldine","family":"Haack","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1146\/annurev-physchem-040513-103724","article-title":"Quantum Heat Engines and Refrigerators: Continuous Devices","volume":"65","author":"Kosloff","year":"2014","journal-title":"Annu. 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