3.1 Concavity of the Entropy Speeds of Propagation in Classical 2.4 Characteristic Speeds

3 Finite Speeds in Non-Relativistic Extended Thermodynamics 

It is shown in this chapter that the concavity of the entropy density tex2html_wrap_inline3415 with respect to the fields tex2html_wrap_inline3353 implies global invertibility of the map tex2html_wrap_inline3613, where tex2html_wrap_inline3615 is the n -vector of Lagrange multipliers. Also the system of field equations - written in terms of tex2html_wrap_inline3481 - is recognized as a symmetric hyperbolic system which guarantees

Thus we conclude that no paradox of infinite speeds can arise in extended thermodynamics, - at least not for finitely many variables.

A commonly treated special case occurs when the fields tex2html_wrap_inline3369 are moments of the phase density of a gas. In this case the pulse speed depends on the degree of extension, i.e. on the number n of fields tex2html_wrap_inline3369 . For a gas in equilibrium the pulse speeds can be calculated for any n . Also it can be estimated that the pulse speed tends to infinity as n grows to infinity.





3.1 Concavity of the Entropy Speeds of Propagation in Classical 2.4 Characteristic Speeds

image Speeds of Propagation in Classical and Relativistic Extended Thermodynamics
Ingo Müller
http://www.livingreviews.org/lrr-1999-1
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