Introduction

Rational extended thermodynamics (RET), Rational extended thermodynamics RET which is compatible with the kinetic theory of gases Kinetic theory and is also closely related to the mathematical theory of hyperbolic systems, Hyperbolic system has been a successful theory of rarefied monatomic gases to explain nonequilibrium phenomena such as light scattering, sound dispersion, shock wave structure, nonequilibrium radiation. These subjects were treated in detail in the book “Rational Extended Thermodynamics” by Ingo Müller Müller, I. and Tommaso Ruggeri Ruggeri, T. . The other subjects remained to be explored in RET were those of polyatomic gases, of dense gases in general, and of mixtures of gases with multi-temperature. This is the aim of the present book to discuss such new RET. In this chapter, before going into the details, we give some introductory perspective on these subjects starting with a short history of nonequilibrium thermodynamics. The new RET theory includes the 14-field theory of dense gases that reduces to the classical Navier-Stokes Fourier theory in the parabolic limit (Maxwellian iteration), to the singular limit of a monatomic gas with 13 fields, and to the subsystem with 6 fields. The 6-field theory is the minimal dissipative system, where the dissipation is only due to the dynamic pressure, after the Euler system of perfect fluids. The concept of nonequilibrium temperature is also discussed. For rarefied polyatomic gases, we discuss a theory of molecular RET with arbitrary number of field variables by using the methods of closure based on both the maximum entropy principle and the entropy principle. It can be proved that the two methods are equivalent to each other. Several applications of the new RET theory are reviewed as well. Moreover we discuss the theory of a mixture of gases Mixture of gases with multi-temperature, Multi-temperature i.e., a mixture in which each constituent has its own temperature. In the new approach, the qualitative analysis of the differential system is also done by taking into account the fact that, due to the convexity of the entropy, there exists a privileged field (main field) such that the system becomes symmetric hyperbolic. Existence of global smooth solutions and convergence to equilibrium are also discussed.