{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T05:33:47Z","timestamp":1762493627556,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T00:00:00Z","timestamp":1762300800000},"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":"crossref","award":["12105361"],"award-info":[{"award-number":["12105361"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Scientific Research Startup Foundation of Civil Aviation University of China","award":["2015QD05X"],"award-info":[{"award-number":["2015QD05X"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The generalized fluctuation\u2013dissipation relations that produce the regularized Kappa distributions are studied. The two-variable Fokker\u2013Planck equation, as well as its reductions in the absence of potential and in the overdamped limit, are considered. All these Fokker\u2013Planck equations have the regularized Kappa distributions as the stationary solutions if the friction and diffusion coefficients satisfy the generalized fluctuation\u2013dissipation relations. In addition, we prove that the principle of detailed balance holds for all the stationary solutions derived in this work.<\/jats:p>","DOI":"10.3390\/e27111138","type":"journal-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T13:19:29Z","timestamp":1762348769000},"page":"1138","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Stochastic Dynamics for the Regularized Kappa-Distributed Plasmas"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0972-537X","authenticated-orcid":false,"given":"Ran","family":"Guo","sequence":"first","affiliation":[{"name":"Department of Physics, College of Science, Civil Aviation University of China, Tianjin 300300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Olbert, S. 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