{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T05:56:55Z","timestamp":1762408615069,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2008,9,24]],"date-time":"2008-09-24T00:00:00Z","timestamp":1222214400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We discuss the different roles of the entropy principle in modern thermodynamics. We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations. Then we discuss the entropy principle for selecting admissible discontinuous weak solutions and to symmetrize general systems of hyperbolic balance laws. A particular attention is given on the local and global well-posedness of the relative Cauchy problem for smooth solutions. Examples are given in the case of extended thermodynamics for rarefied gases and in the case of a multi-temperature mixture of fluids.<\/jats:p>","DOI":"10.3390\/e10030319","type":"journal-article","created":{"date-parts":[[2008,9,29]],"date-time":"2008-09-29T05:43:40Z","timestamp":1222667020000},"page":"319-333","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["The Entropy Principle from Continuum Mechanics to Hyperbolic Systems of Balance Laws: The Modern Theory of Extended Thermodynamics"],"prefix":"10.3390","volume":"10","author":[{"given":"Tommaso","family":"Ruggeri","sequence":"first","affiliation":[{"name":"Department of Mathematics and Research Center of Applied Mathematics (CIRAM), University of Bologna, Via Saragozza 8, 40123 Bologna, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2008,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BF01262690","article-title":"The thermomechanics of elastic materials with heat conduction and viscosity","volume":"13","author":"Coleman","year":"1963","journal-title":"Arch. 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