{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:40:46Z","timestamp":1760244046894,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2008,10,15]],"date-time":"2008-10-15T00:00:00Z","timestamp":1224028800000},"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>Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments.<\/jats:p>","DOI":"10.3390\/e10040477","type":"journal-article","created":{"date-parts":[[2008,10,15]],"date-time":"2008-10-15T04:43:28Z","timestamp":1224045808000},"page":"477-492","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations"],"prefix":"10.3390","volume":"10","author":[{"given":"Ingo","family":"M\u00fcller","sequence":"first","affiliation":[{"name":"Technical University Berlin, Berlin, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2008,10,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"M\u00fcller, I., and Ruggeri, T. (1998). Rational Extended Thermodynamics, Springer Tracts of Natural Philosophy, Springer Verlag. [2nd ed.].","DOI":"10.1007\/978-1-4612-2210-1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/BF00250688","article-title":"Method of Lagrange multipliers for the exploitation of the entropy principle","volume":"46","author":"Liu","year":"1972","journal-title":"Arch. Ration. Mech. An."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"M\u00fcller, I. (1967). Zum Paradox der W\u00e4rmeleitungstheorie. Z. Phys., 198\u2013329.","DOI":"10.1007\/BF01326412"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Kawashima, S. (1987). Large-time behaviour of solutions to hyperbolic-parabolic systems of conservations laws and applications. Proc. Roy. Soc. Edinburgh Sect. 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