Comparison shows that we must have
and hence, by differentiation with respect to ,
Therefore symmetric hyperbolicity of the system (34) and hence the concavity of the entropy density with respect to the variables is implied by the moment character of the fields and the form of the four-flux of entropy.
For a non-degenerate gas the term in the denominator of (38) may be neglected. In that case we have
We know that a non-degenerate gas at rest in equilibrium exhibits the Maxwellian phase densityn and denote the number density and the temperature of the gas in equilibrium. Comparison of (43) with (40) shows that only two Lagrange multipliers are non-zero in equilibrium, viz.
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