{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T21:33:15Z","timestamp":1761514395356,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T00:00:00Z","timestamp":1558051200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 11775084"],"award-info":[{"award-number":["No. 11775084"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science","award":["No. 16K05484"],"award-info":[{"award-number":["No. 16K05484"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A general comment is made on the existence of various baths in quantum thermodynamics, and a brief explanation is presented about the concept of weak invariants. Then, the isoenergetic process is studied for a spin in a magnetic field that slowly varies in time. In the Markovian approximation, the corresponding Lindbladian operators are constructed without recourse to detailed information about the coupling of the subsystem with the environment called the energy bath. The entropy production rate under the resulting Lindblad equation is shown to be positive. The leading-order expressions of the power output and work done along the isoenergetic process are obtained.<\/jats:p>","DOI":"10.3390\/e21050503","type":"journal-article","created":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T11:06:46Z","timestamp":1558091206000},"page":"503","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Spin Isoenergetic Process and the Lindblad Equation"],"prefix":"10.3390","volume":"21","author":[{"given":"Congjie","family":"Ou","sequence":"first","affiliation":[{"name":"Physics Division, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuho","family":"Yokoi","sequence":"additional","affiliation":[{"name":"Department of Physical Engineering, Mie University, Mie 514-8507, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sumiyoshi","family":"Abe","sequence":"additional","affiliation":[{"name":"Physics Division, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China"},{"name":"Department of Physical Engineering, Mie University, Mie 514-8507, Japan"},{"name":"Institute of Physics, Kazan Federal University, 420008 Kazan, Russia"},{"name":"ESIEA, 9 Rue Vesale, 75005 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"012113","DOI":"10.1103\/PhysRevE.96.012113","article-title":"Interplay of different environments in open quantum systems: Breakdown of the additive approximation","volume":"96","author":"Giusteri","year":"2017","journal-title":"Phys. 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