the entropy principle from continuum mechanics to hyperbolic systems of balance laws the modern theory of extended thermodynamics从连续介质力学双曲系统的熵原理平衡热力学法的现代理论扩展.pdf

Entropy 2008, 10, 319-333; DOI: 10.3390/ OPEN ACCESS entropy ISSN 1099-4300 Article /entropy The Entropy Principle from Continuum Mechanics to Hyperbolic Systems of Balance Laws: The Modern Theory of Extended Thermodynamics Tommaso Ruggeri 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 Abstract: We discuss the different roles of the entropy principle in modern thermodynam- ics. 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. 1. Entropy principle in continuum mechanics The concept and name of entropy originated in the early 1850’s in the work of Rudolf Julius Emanuel Clausius (1822-1888): ”Heat cannot pass by itself from a cold to a hot body”. In the classical approach of thermodynamics (the theory of non-equilibrium