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Entropy 2008, 10(3), 319-333; doi:10.3390/e10030319

The Entropy Principle from Continuum Mechanics to Hyperbolic Systems of Balance Laws: The Modern Theory of Extended Thermodynamics

Department of Mathematics and Research Center of Applied Mathematics (CIRAM), University of Bologna, Via Saragozza 8, 40123 Bologna, Italy
Received: 3 May 2008 / Accepted: 4 September 2008 / Published: 24 September 2008
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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.
Keywords: Entropy Principle; Non-Equilibrium Thermodynamics; Hyperbolic Systems of Balance Laws Entropy Principle; Non-Equilibrium Thermodynamics; Hyperbolic Systems of Balance Laws
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Ruggeri, T. The Entropy Principle from Continuum Mechanics to Hyperbolic Systems of Balance Laws: The Modern Theory of Extended Thermodynamics. Entropy 2008, 10, 319-333.

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