{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T14:10:47Z","timestamp":1775484647659,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,2,15]],"date-time":"2018-02-15T00:00:00Z","timestamp":1518652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100007364","name":"Fondazione CRT","doi-asserted-by":"publisher","award":["ERC project support"],"award-info":[{"award-number":["ERC project support"]}],"id":[{"id":"10.13039\/100007364","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010661","name":"H2020","doi-asserted-by":"publisher","award":["MODCOMP project (G.A. 685844)"],"award-info":[{"award-number":["MODCOMP project (G.A. 685844)"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this work, we derive different systems of mesoscopic moment equations for the heat-conduction problem and analyze the basic features that they must hold. We discuss two- and three-equation systems, showing that the resulting mesoscopic equation from two-equation systems is of the telegraphist\u2019s type and complies with the Cattaneo equation in the Extended Irreversible Thermodynamics Framework. The solution of the proposed systems is analyzed, and it is shown that it accounts for two modes: a slow diffusive mode, and a fast advective mode. This latter additional mode makes them suitable for heat transfer phenomena on fast time-scales, such as high-frequency pulses and heat transfer in small-scale devices. We finally show that, if proper initial conditions are provided, the advective mode disappears, and the solution of the system tends asymptotically to the transient solution of the classical parabolic heat-conduction equation.<\/jats:p>","DOI":"10.3390\/e20020126","type":"journal-article","created":{"date-parts":[[2018,2,20]],"date-time":"2018-02-20T03:54:22Z","timestamp":1519098862000},"page":"126","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Mesoscopic Moment Equations for Heat Conduction: Characteristic Features and Slow\u2013Fast Mode Decomposition"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6130-9544","authenticated-orcid":false,"given":"Luca","family":"Bergamasco","sequence":"first","affiliation":[{"name":"Energy Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy"}]},{"given":"Matteo","family":"Alberghini","sequence":"additional","affiliation":[{"name":"Energy Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3997-3681","authenticated-orcid":false,"given":"Matteo","family":"Fasano","sequence":"additional","affiliation":[{"name":"Energy Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy"}]},{"given":"Annalisa","family":"Cardellini","sequence":"additional","affiliation":[{"name":"Energy Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6165-7434","authenticated-orcid":false,"given":"Eliodoro","family":"Chiavazzo","sequence":"additional","affiliation":[{"name":"Energy Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1814-3846","authenticated-orcid":false,"given":"Pietro","family":"Asinari","sequence":"additional","affiliation":[{"name":"Energy Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jou, D., Casas-V\u00e1zquez, J., and Lebon, G. 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