Level of Description and Internal Variables

The choice of constitutive equations means in fact the choice of such properties the natural scales of which are comparable with the observer s scales. Quantities the natural scales of which are much greater than the observer s scale play a role of constant parameters in constitutive equations (they are in frozen equilibrium or uniform) on the other hand, quantities with a much shorter natural scale than the observer s may be regarded as in ( relaxed ) equilibrium or having localized influence through their gradients. 

We discuss the level of description on uniform fluid models from Chap. 2. Here the space gradients have no influence (observer s space scales are much less than the natural space scales) and therefore we discuss only the time scales. Different constitutive models may be applied on the same physical system, say models A, B, C, D in Sect. 2.2 on a uniform, closed fluid body. This corresponds to the use of various observer s scales relative to the same natural time scales which are in this 

The following results are obviously valid locally in nonuniform systems of Chaps. 3,4. Moreover, space scales may be discussed analogously, cf. similarity of differential memory with local action in Sect. 3.5. 

Processes in model A (which are all the equilibrium processes here, cf. Sect. 2.2) may be regarded as the time sequence of equilibrium states (in the sense of S4 in Sect. 1.2) because the infinitesimal instant (in fact the time interval between adjoining states) in A is greater than the natural scale (relaxation time) of quantities V, T which are in (relaxed) equilibrium, see also Rem. 48 in Chap. 3. 

Only a part of processes in model B is the equilibrium process (2.28) because only T (but not V) is in relaxed equilibrium, (see Rem. 9). Such a limitation is more severe for models C, D where neither T nor V are relaxed in corresponding equilibrium processes. 

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