Recent Bibliography On Extended Irreversible Thermodynamics and Related Topics (1992-1995)

Abstract

We present a list of the references on extended irreversible thermodynamics and closely related topics published between May 1992 and May 1995, and we provide some general comments about the main open problems, applications and prospects in this field. This list complements our previous bibliographical review on this topic published in by several researchers working in this field. Since 1993, four books have appeared which are closely related to extended irreversible thermodynamics [45,83,126,164]. These books are rather different in their aims and scopes, but they rest on the same basic idea to extend the space of variables by including the fluxes as independent variables. Two of the books [83,126] are directly concerned with extended irreversible thermodynamics and provide global and systematic approaches to this subject. The book by Jou, Casas-Vazquez and Lebon [83] is based on techniques which are similar to those used in classical irreversible thermodynamics; the microscopic foundations of the theory are discussed from the points of view of kinetic theory of ideal and real gases, fluctuation and information theory, and applications to hyperbolic heat transport and phonon hydrodynamics, rheology, ultrasounds and shock waves in gases, generalized hydrodynamics, numerical simulations, multicomponent systems (including the analysis of phase diagrams of polymer solutions under shear and electrical systems), are also proposed as well as a relativistic approach with applications to cosmological models. Furthermore, each chapter includes several proposed problems, some of them based on recent research literature. The monograph by Müller and Ruggeri [126] uses methods similar to those of rational thermodynamics (in the formalism of Lagrange multipliers devised by Shi-Liu), and has a more mathematical character than the previous book [83]: it relates the macroscopic theory to the kinetic theory of ideal gases, it pays much attention to the properties of wave propagation and shock waves in solids (phonon system) and in radiation; one can also find an analysis of generalized hydrodynamics, and a relativistic formulation of the theory. Though the approaches followed in [83] and [126] differ, they yield rather similar conclusions concerning the essential points.The two other mentioned monographs are not centered on extended thermodynamics but they refer to it in a substantial part of the text. The book by Eu [45] starts from the kinetic theory and presents his generalized moment method, with a wide range of applications. This book reserves the name of entropy to the Boltzmann entropy, rather than to the macroscopic, phenomenological entropy used in extended thermodynamics, which receives in this book a different name. Therefore, it may be surprising for the reader to learn that the entropy is no longer function of state, in contrast to the assumptions introduced in [83] and [126]. In fact, as it has been recognised by the author of the book [48,49], there is not an unsurmountable contradiction between the different points...

A Special Relativistic Exploitation of the Second Law of Thermodynamics and Its Non-Relativistic Limit

“…Relativistic TIP was generalized to mixtures of different chemical components [ 2 , 3 , 4 ] and to systems with polarization and magnetization [ 5 ]. For a review of the problems and possible solutions of special- and general-relativistic TIP see [ 6 ] and for an overview over the literature on relativistic TIP [ 7 , 8 ].…”

A mesoscopic approach to diffusion phenomena in mixtures

“…The last paradox must be overcome by considering non-Fickian transport behavior for the diffusive mass flux. A possible solution is given in Extended Thermodynamics [1,2,3,4,5]. The diffusion flux is introduced as an additional field variable, obeying a differential equation.…”