Constitutive theory

5.2 Constitutive theory

We recall the restrictive principles of the constitutive theory from Section 2 and adjust them to the present case

entropy inequality $hA ≥ 0 ,A$ with $hA = ˆhA(AM ,AMN )$ ,
principle of relativity.

The former principle was discussed and exploited in the general scheme of Section 2, but the principle of relativity was not. This principle assumes that the constitutive functions $ˆ ABC A$ , $ˆAB I$ , $ˆ A h$ – generically $Cˆ$ – are invariant under Lorentz transformations

∗A ∗A B x = x (x ).

Thus the principle of relativity may be stated in the form

Note that $ˆ C$ is the same function in both equations.

It is complicated and cumbersome to exploit the constitutive theory but the results are remarkably specific, at least for near-equilibrium processes:

$ˆAABC$ will be reduced to the thermal equation of state.
$ˆAB I$ will be reduced to the relaxation times of the gas, which may be considered to be of the order of magnitude of the mean time of free flight of its molecules.

For details of the calculation the reader is referred to the literature, in particular to the book by Müller & Ruggeri [39 , 40 ] or the paper by Liu, Müller & Ruggeri [31 ]. Here we explain only the results.