Speeds of Propagation in Classical and Relativistic Extended Thermodynamics
The Navier-Stokes-Fourier theory of viscous, heat-conducting fluids provides parabolic equations and thus predicts infinite pulse speeds. Naturally this feature has disqualified the theory for relativistic thermodynamics which must insist on finite speeds and, moreover, on speeds smaller than c. The...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer International Publishing
1999
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5255572/ https://www.ncbi.nlm.nih.gov/pubmed/28191828 http://dx.doi.org/10.12942/lrr-1999-1 |
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author | Müller, Ingo |
author_facet | Müller, Ingo |
author_sort | Müller, Ingo |
collection | PubMed |
description | The Navier-Stokes-Fourier theory of viscous, heat-conducting fluids provides parabolic equations and thus predicts infinite pulse speeds. Naturally this feature has disqualified the theory for relativistic thermodynamics which must insist on finite speeds and, moreover, on speeds smaller than c. The attempts at a remedy have proved heuristically important for a new systematic type of thermodynamics: Extended thermodynamics. That new theory has symmetric hyperbolic field equations and thus it provides finite pulse speeds. Extended thermodynamics is a whole hierarchy of theories with an increasing number of fields when gradients and rates of thermodynamic processes become steeper and faster. The first stage in this hierarchy is the 14-field theory which may already be a useful tool for the relativist in many applications. The 14 fields — and further fields — are conveniently chosen from the moments of the kinetic theory of gases. The hierarchy is complete only when the number of fields tends to infinity. In that case the pulse speed of non-relativistic extended thermodynamics tends to infinity while the pulse speed of relativistic extended thermodynamics tends to c, the speed of light. In extended thermodynamics symmetric hyperbolicity — and finite speeds — are implied by the concavity of the entropy density. This is still true in relativistic thermodynamics for a privileged entropy density which is the entropy density of the rest frame for non-degenerate gases. |
format | Online Article Text |
id | pubmed-5255572 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 1999 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-52555722017-02-06 Speeds of Propagation in Classical and Relativistic Extended Thermodynamics Müller, Ingo Living Rev Relativ Review Article The Navier-Stokes-Fourier theory of viscous, heat-conducting fluids provides parabolic equations and thus predicts infinite pulse speeds. Naturally this feature has disqualified the theory for relativistic thermodynamics which must insist on finite speeds and, moreover, on speeds smaller than c. The attempts at a remedy have proved heuristically important for a new systematic type of thermodynamics: Extended thermodynamics. That new theory has symmetric hyperbolic field equations and thus it provides finite pulse speeds. Extended thermodynamics is a whole hierarchy of theories with an increasing number of fields when gradients and rates of thermodynamic processes become steeper and faster. The first stage in this hierarchy is the 14-field theory which may already be a useful tool for the relativist in many applications. The 14 fields — and further fields — are conveniently chosen from the moments of the kinetic theory of gases. The hierarchy is complete only when the number of fields tends to infinity. In that case the pulse speed of non-relativistic extended thermodynamics tends to infinity while the pulse speed of relativistic extended thermodynamics tends to c, the speed of light. In extended thermodynamics symmetric hyperbolicity — and finite speeds — are implied by the concavity of the entropy density. This is still true in relativistic thermodynamics for a privileged entropy density which is the entropy density of the rest frame for non-degenerate gases. Springer International Publishing 1999-06-14 1999 /pmc/articles/PMC5255572/ /pubmed/28191828 http://dx.doi.org/10.12942/lrr-1999-1 Text en © The Author(s) 1999 |
spellingShingle | Review Article Müller, Ingo Speeds of Propagation in Classical and Relativistic Extended Thermodynamics |
title | Speeds of Propagation in Classical and Relativistic Extended Thermodynamics |
title_full | Speeds of Propagation in Classical and Relativistic Extended Thermodynamics |
title_fullStr | Speeds of Propagation in Classical and Relativistic Extended Thermodynamics |
title_full_unstemmed | Speeds of Propagation in Classical and Relativistic Extended Thermodynamics |
title_short | Speeds of Propagation in Classical and Relativistic Extended Thermodynamics |
title_sort | speeds of propagation in classical and relativistic extended thermodynamics |
topic | Review Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5255572/ https://www.ncbi.nlm.nih.gov/pubmed/28191828 http://dx.doi.org/10.12942/lrr-1999-1 |
work_keys_str_mv | AT mulleringo speedsofpropagationinclassicalandrelativisticextendedthermodynamics |