In the relativistic theory the entropy density is not a scalar, it depends on the frame. This fact creates problems: Granted that an entropy density tends to be concave, which one would that be? To my knowledge this question is unresolved. In this section we assume that there exists a privileged frame in which the entropy density is concave. And we choose the privileged frame such that symmetric hyperbolicity of the system of field equations is guaranteed. These considerations have been motivated by a paper by Ruggeri [42].

Symmetric hyperbolicity means finite characteristic speeds, not necessarily speeds smaller than the speed of light. However, for moments as four-fluxes it can be shown that all speeds are smaller or equal to c and that for infinitely many moments the pulse speed tends to c. Moreover, for moments the privileged frame is the rest frame of the gas, at least, if the gas is non-degenerate.

4.1 Concavity of a privileged entropy density

4.2 Symmetric hyperbolicity

4.3 Moments as four-fluxes and the vector potential

4.4 Upper and lower bounds for the pulse speed

4.2 Symmetric hyperbolicity

4.3 Moments as four-fluxes and the vector potential

4.4 Upper and lower bounds for the pulse speed

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