We have defined and is the molecular rest mass.
The decomposition (86) is not only popular because of its intuitive quality but also, since it is now possible to characterize equilibrium as a process in which the stress deviator , the heat flux and the dynamic pressure – the non-equilibrium part of the pressure – vanish.
The equilibrium pressure is a function of and , the thermal equation of state. In thermodynamics it is often useful to replace the variables by
because these two variables can be measured – at least in principle. Also and are the natural variables of statistical thermodynamics which provides the thermal equation of state in the form . The transition between the new variables and the old ones can be effected by the relations
If we restrict attention to a linear theory in , , and , we can satisfy the principle of relativity with linear isotropic functions for , viz.
The ’s in (90) are restricted by inequalities, viz.
In conclusion we may write the field equations in the form
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