{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T03:34:08Z","timestamp":1773545648425,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,2,12]],"date-time":"2018-02-12T00:00:00Z","timestamp":1518393600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["2015\/19\/B\/ST2\/02856"],"award-info":[{"award-number":["2015\/19\/B\/ST2\/02856"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We consider a paradigmatic model of a quantum Brownian particle coupled to a thermostat consisting of harmonic oscillators. In the framework of a generalized Langevin equation, the memory (damping) kernel is assumed to be in the form of exponentially-decaying oscillations. We discuss a quantum counterpart of the equipartition energy theorem for a free Brownian particle in a thermal equilibrium state. We conclude that the average kinetic energy of the Brownian particle is equal to thermally-averaged kinetic energy per one degree of freedom of oscillators of the environment, additionally averaged over all possible oscillators\u2019 frequencies distributed according to some probability density in which details of the particle-environment interaction are present via the parameters of the damping kernel.<\/jats:p>","DOI":"10.3390\/e20020123","type":"journal-article","created":{"date-parts":[[2018,2,12]],"date-time":"2018-02-12T11:16:09Z","timestamp":1518434169000},"page":"123","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Kinetic Energy of a Free Quantum Brownian Particle"],"prefix":"10.3390","volume":"20","author":[{"given":"Pawe\u0142","family":"Bialas","sequence":"first","affiliation":[{"name":"Institute of Physics, University of Silesia, 41-500 Chorz\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2296-4532","authenticated-orcid":false,"given":"Jerzy","family":"\u0141uczka","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Silesia, 41-500 Chorz\u00f3w, Poland"},{"name":"Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorz\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,12]]},"reference":[{"key":"ref_1","unstructured":"Terletski\u00ed, Y.P. 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