The tools of the constitutive theory are certain universal physical principles which have come to be accepted by the extrapolation of common experience. Above all there are three such principles:
This inequality is clearly an extrapolation of the entropy inequalities known in thermostatics and thermodynamics of irreversible processes; it was first stated in this generality by Müller [36, 38].
The formal statement and exploitation of this principle have
to await a specific choice for the fields
and the four-fluxes
.
It is possible, and indeed common, to make a specific
choice for the fields
and the concavity postulate is contingent upon that
choice.
The privileged co-vector
remains to be chosen, see Section
4.1
.
In both cases the concavity postulate makes it possible that the entropy be maximal for a particular set of fields - the set corresponding to equilibrium - and that is its attraction for physicists. For mathematicians the attraction of the concavity postulate lies in the observation that concavity implies symmetric hyperbolicity of the field equations, see Sections 3.2 and 4.2 below.
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Speeds of Propagation in Classical and Relativistic
Extended Thermodynamics
Ingo Müller http://www.livingreviews.org/lrr-1999-1 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |