Alternative mathematical theory of non-equilibrium phenomena (Q1381098)

This book is inspired on Falk's generalization, carried out in the 1970's, of the Gibbs mathematical formulation of thermodynamics. Falk's contribution implies to eliminate the so-called ``metaphysical elements'' in physics, understanding that the usual formulations of the first and second laws of thermodynamics are ``metaphysical'' because they demand in principle an infinite number of data for their verification. In practice, the crucial differences between classical and alternative theories are the concept of non-equilibrium state, described by a special vector function -- named dissipation velocity -- and the exclusion of the classical separation between a kinematic and a thermodynamic part (or a mechanical and an electromagnetic part). The book has a strong emphasis on philosophical aspects, with the aim to clarify the connection between the physically measured variables and reality. One of the subjects discussed in most detail is the relation between the ``thermodynamic particles'' constituting a macroscopic system and the microscopic entities (atoms, molecules) which form it. The main consequence of this discussion is the definition of the macroscopic momentum of the system, which according to the author is far subtler than the plain addition of mivi (mi and vi being the mass and speed of the microscopic particles), and depends on all the relevant macroscopic variables of the system. An important consequence is that the state of a macroscopic system in motion cannot be radically separated from the description of its thermodynamic state. The theory of nonequilibrium phenomena proposed in this book takes into account this mutual dependence of macroscopic speed and macroscopic thermodynamic state in such a way that the local-equilibrium hypothesis is no longer taken for granted. A so-called dissipative velocity is considered which takes into account non-local equilibrium effects and modifies the conventional concept of the mass-point momentum. The conditions are examined under which the resulting expression for the pressure tensor becomes independent of the local state of motion, thus allowing to substitute the pressure of a fluid by the equation of state valid at rest. The balance equation of entropy density leads to a revised version of the constitutive equations which reduce to the classical ones when the system obeys the local-equilibrium requirements. The book is composed of nine chapters and three appendices. The first chapter reviews the importance of non-equilibrium phenomena in the contemporary physics, and describes the continuum theories of mass-point fluids. Chapter 2 is an introduction to Falkian dynamics. Chapters 3 and 4 discuss basic questions on motion and matter -- mainly the so-called Callen's principle for the choice of the macroscopic variables, and the relation between the description of energy-momentum transport and the model assumed for the matter --, and on the symmetries of the systems and their connection with conservation laws. Chapter 5 generalizes the ideas previously presented to multicomponent systems. Chapters 6 and 7 play a central role, by introducing the essential elements of the alternative description -- especially the dissipation velocity -- and its connection with constitutive properties of the matter and with the equation of motion -- for instance, for viscous systems this theory yields a Navier-Saint Venant equation which reduces to Navier-Stokes equation in some circumstances. Chapters 8 and 9 complement the illustrations with the consideration of turbulence, shock waves and other complex flow phenomena, and with a short presentation of electromagnetic phenomena in continua. The appendices deal with historical aspects of atomism, and with mathematical supplements and computational schemes. One has the impression that the philosophical discussion has been given far more extension than the explicit physical consequences. More comparisons with the classical local-equilibrium theory and other more general theories in some simple specific examples would have been useful for researchers acquainted with those theories but unaware up to now of the one presented in this book, which has certainly appealing to aspects whose domain of validity and whose practical advantages are not yet clear.