Abstract
We discuss the different roles of the entropy principle in modern thermodynamics. We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations. Then we discuss the entropy principle for selecting admissible discontinuous weak solutions and to symmetrize general systems of hyperbolic balance laws. A particular attention is given on the local and global well-posedness of the relative Cauchy problem for smooth solutions. Examples are given in the case of extended thermodynamics for rarefied gases and in the case of a multi-temperature mixture of fluids.
Highlights
Entropy principle in continuum mechanicsThe concept and name of entropy originated in the early 1850’s in the work of Rudolf Julius Emanuel
We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations
S, p, ε and ρ comes as a consequence of the entropy principle and is not assumed a priori as in the thermodynamics of irreversible process (TIP)
Summary
The concept and name of entropy originated in the early 1850’s in the work of Rudolf Julius Emanuel. In the classical approach of thermodynamics (the theory of non-equilibrium processes), the entropy principle characterizes the irreversibility of the processes, i.e. an arrow in the time direction. T with T denoting the absolute temperature and S the entropy density given by a constitutive relation to be determined by the compatibility between the balance Eqs. and (1). S, p, ε and ρ comes as a consequence of the entropy principle and is not assumed a priori as in the thermodynamics of irreversible process (TIP) (local equilibrium assumption). In the modern rational thermodynamics the entropy principle becomes a constraint for the acceptable constitutive equations. At the present the general form (4) is universally accepted in the continuum mechanics community and all the constitutive equations in new models are tested by the entropy principle
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