{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T01:18:34Z","timestamp":1773537514584,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,13]],"date-time":"2017-07-13T00:00:00Z","timestamp":1499904000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted fluid by means of self-propulsion. Energy injected by such a non-equilibrium force is eventually dissipated as heat in the thermostat. Since thermal fluctuations are much faster and weaker than self-propulsion forces, they are often neglected, blurring the identification of dissipated heat in theoretical models. For the same reason, some freedom\u2014or arbitrariness\u2014appears when defining entropy production. Recently three different recipes to define heat and entropy production have been proposed for the same model where the role of self-propulsion is played by a Gaussian coloured noise. Here we compare and discuss the relation between such proposals and their physical meaning. One of these proposals takes into account the heat exchanged with a non-equilibrium active bath: such an \u201cactive heat\u201d satisfies the original Clausius relation and can be experimentally verified.<\/jats:p>","DOI":"10.3390\/e19070356","type":"journal-article","created":{"date-parts":[[2017,7,13]],"date-time":"2017-07-13T10:31:57Z","timestamp":1499941917000},"page":"356","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":49,"title":["Clausius Relation for Active Particles: What Can We Learn from Fluctuations"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7229-9457","authenticated-orcid":false,"given":"Andrea","family":"Puglisi","sequence":"first","affiliation":[{"name":"CNR-ISC and Dipartimento di Fisica, Sapienza Universit\u00e0 di Roma, p.le A. Moro 2, 00185 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2764-8259","authenticated-orcid":false,"given":"Umberto","family":"Marini Bettolo Marconi","sequence":"additional","affiliation":[{"name":"Scuola di Scienze e Tecnologie, Universit\u00e0 di Camerino, Via Madonna delle Carceri, 62032 Camerino, Italy"},{"name":"Istituto Nazionale di Fisica Nucleare (INFN), Perugia 06123, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1146\/annurev-conmatphys-070909-104101","article-title":"The Mechanics and Statistics of Active Matter","volume":"1","author":"Ramaswamy","year":"2010","journal-title":"Annu. Rev. Condens. 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