{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T07:07:37Z","timestamp":1769584057114,"version":"3.49.0"},"reference-count":205,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,20]],"date-time":"2023-07-20T00:00:00Z","timestamp":1689811200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"resolution of the Academic Senate","award":["56199"],"award-info":[{"award-number":["56199"]}]},{"name":"resolution of the Academic Senate","award":["56210"],"award-info":[{"award-number":["56210"]}]},{"name":"FFABR Unime 2019","award":["56199"],"award-info":[{"award-number":["56199"]}]},{"name":"FFABR Unime 2019","award":["56210"],"award-info":[{"award-number":["56210"]}]},{"name":"FFABR Unime 2022","award":["56199"],"award-info":[{"award-number":["56199"]}]},{"name":"FFABR Unime 2022","award":["56210"],"award-info":[{"award-number":["56210"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this review, we discuss a nonequilibrium thermodynamic theory for heat transport in superlattices, graded systems, and thermal metamaterials with defects. The aim is to provide researchers in nonequilibrium thermodynamics as well as material scientists with a framework to consider in a systematic way several nonequilibrium questions about current developments, which are fostering new aims in heat transport, and the techniques for achieving them, for instance, defect engineering, dislocation engineering, stress engineering, phonon engineering, and nanoengineering. We also suggest some new applications in the particular case of mobile defects.<\/jats:p>","DOI":"10.3390\/e25071091","type":"journal-article","created":{"date-parts":[[2023,7,21]],"date-time":"2023-07-21T01:52:35Z","timestamp":1689904355000},"page":"1091","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Non-Equilibrium Thermodynamics of Heat Transport in Superlattices, Graded Systems, and Thermal Metamaterials with Defects"],"prefix":"10.3390","volume":"25","author":[{"given":"David","family":"Jou","sequence":"first","affiliation":[{"name":"Grup de Fis\u00edca Estad\u00edstica, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Spain"},{"name":"Institut d\u2019Estudis Catalans, Carme, 47, 08001 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7251-6175","authenticated-orcid":false,"given":"Liliana","family":"Restuccia","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d\u2019Alcontres, 31, 98166 Messina, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/0001-6160(61)90057-8","article-title":"Dislocation configurations in AuCu3 and AuCu type superlattices","volume":"9","author":"Marcinkowski","year":"2016","journal-title":"Acta Metall."},{"key":"ref_2","first-page":"100","article-title":"Dislocation filtering in semiconductor superlattices with lattice-matched and lattice- mismatched layer materials","volume":"49","author":"Gowley","year":"1986","journal-title":"Appl. Phys. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1557\/PROC-148-217","article-title":"The use of superlattices to block the propagation of dislocations in semiconductors","volume":"148","author":"Blakeslee","year":"1989","journal-title":"MRS Online Proc. 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