{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,11]],"date-time":"2026-10-11T13:40:15Z","timestamp":1791726015872,"version":"4.3.4"},"reference-count":76,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,5]],"date-time":"2021-01-05T00:00:00Z","timestamp":1609804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003407","name":"MIUR","doi-asserted-by":"publisher","award":["201798CZLJ"],"award-info":[{"award-number":["201798CZLJ"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009880","name":"Regione Lazio","doi-asserted-by":"publisher","award":["85-2017-15257"],"award-info":[{"award-number":["85-2017-15257"]}],"id":[{"id":"10.13039\/501100009880","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein\u2013Uhlenbeck particle (AOUP) model. We express the linear response in terms of correlations computed in the absence of perturbations, proposing a particularly compact and readable fluctuation\u2013dissipation relation (FDR): such an expression explicitly separates equilibrium and non-equilibrium contributions due to self-propulsion. As a case study, we consider non-interacting AOUP confined in single-well and double-well potentials. In the former case, we also unveil the effect of dimensionality, studying one-, two-, and three-dimensional dynamics. We show that information about the distance from equilibrium can be deduced from the FDR, putting in evidence the roles of position and velocity variables in the non-equilibrium relaxation.<\/jats:p>","DOI":"10.3390\/sym13010081","type":"journal-article","created":{"date-parts":[[2021,1,5]],"date-time":"2021-01-05T11:51:39Z","timestamp":1609847499000},"page":"81","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":46,"title":["Fluctuation\u2013Dissipation Relations in Active Matter Systems"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1384-0917","authenticated-orcid":false,"given":"Lorenzo","family":"Caprini","sequence":"first","affiliation":[{"name":"School of Sciences and Technology, University of Camerino, Via Madonna delle Carceri, I-62032 Camerino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7229-9457","authenticated-orcid":false,"given":"Andrea","family":"Puglisi","sequence":"additional","affiliation":[{"name":"Institute for Complex Systems\u2014CNR, P.le Aldo Moro 2, 00185 Rome, Italy"},{"name":"Department of Physics, University of Rome Sapienza, P.le Aldo Moro 2, 00185 Rome, Italy"},{"name":"INFN, University of Rome Tor Vergata, Via della Ricerca Scientiica 1, 00133 Rome, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3686-0822","authenticated-orcid":false,"given":"Alessandro","family":"Sarracino","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Campania \u201cLuigi Vanvitelli\u201d, Caserta, 81031 Aversa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1103\/PhysRev.37.405","article-title":"Reciprocal Relations in Irreversible Processes. 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