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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Autor principal: Müller, Ingo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 1999
Materias:
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
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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.
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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