5 Relativistic Thermodynamics of Gases. 5.6 Characteristic Speeds in a

5.7 Discussion 

So as to anticipate a possible misunderstanding I remark that the equations (93Popup Equation, 94Popup Equation, 95Popup Equation) with tex2html_wrap_inline4503 from (89Popup Equation) and (91Popup Equation) are neither symmetric nor fully hyperbolic. Indeed the underlying symmetry of the system (79Popup Equation, 80Popup Equation, 81Popup Equation), and  (84Popup Equation) reveals itself only when the Lagrange multipliers tex2html_wrap_inline3481 are used as variables. But (93Popup Equation, 94Popup Equation, 95Popup Equation, 89Popup Equation, 91Popup Equation) are equations for the physical variables tex2html_wrap_inline4507 or in fact tex2html_wrap_inline4509, and tex2html_wrap_inline4335 . Also the hyperbolicity in the whole state space is lost, because the equations (89Popup Equation, 90Popup Equation) are restricted to linear terms. Therefore the system is hyperbolic only in the neighbourhood of equilibrium. For a more detailed discussion of these aspects, see Müller & Ruggeri [39, 40].

5 Relativistic Thermodynamics of Gases. 5.6 Characteristic Speeds in a

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