On The Foundations Of Equilibrium Relativistic Kinetic Theory And Applications

The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.

Relativistic kinetic theory has widespread application in astrophysics and cosmology. The interest has grown in recent years as experimentalists are now able to make reliable measurements on physical systems where relativistic effects are no longer negligible. This ambitious monograph is divided into three parts. It presents the basic ideas and concepts of this theory, equations and methods, including derivation of kinetic equations from the relativistic BBGKY hierarchy and discussion of the relation between kinetic and hydrodynamic levels of description. The second part introduces elements of computational physics with special emphasis on numerical integration of Boltzmann equations and related approaches, as well as multi-component hydrodynamics. The third part presents an overview of applications ranging from covariant theory of plasma response, thermalization of relativistic plasma, comptonization in static and moving media to kinetics of self-gravitating systems, cosmological structure formation and neutrino emission during the gravitational collapse.

This book presents fundamentals, equations, and methods of solutions of relativistic kinetic theory, with applications in astrophysics and cosmology.

This book goes beyond the scope of other works in the field with its thorough treatment of applications in a wide variety of disciplines. The third edition features a new section on constants of motion and symmetry and a new appendix on the Lorentz-Legendre expansion.

Covers a wide spectrum of applications and contains a wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The new edition reflects new developments and contains a new chapter on the interplay between hydrodynamics and thermodynamics.

This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on nonrelativistic contexts, it provides a comprehensive picture of the relativistic covariant kinetic theory of gases and relativistic hydrodynamics of gases.Relativistic theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids). They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respect to macroscopic fluxes or thermodynamic forces. The irreversible covariant Boltzmann as well as the covariant form of the Boltzmann-Nordheim-Uehling-Uhlenbeck equation is used for deriving theories of irreversible transport equations and generalized hydrodynamic equations for either classical gases or quantum gases. They all conform rigorously to the tenet. All macroscopic observables described by the so-formulated theories therefore are likewise expected to strictly obey the tenet.

Modern technology strives towards higher speed, higher power, and higher miniaturiza tion. In these conditions, the classical transport equations must be updated in order to incorporate memory, non-local, and non-linear effects. These effects have been studied by starting from microscopic models which are specific to particular systems and whose solution requires mathematical approximations and boundary conditions. The aim of extended irreversible thermodynamics is to complement such microscopic analyses with a macroscopic framework which could play, with respect to the generalized trans port equations incorporating the aforementioned effects, a role similar to the one played by classical thermodynamics with respect to the classical transport equations. Such a macroscopic framework is particularly useful for comparing the results obtained from various microscopic models, for placing some restrictions on the range of validity of different approximations, and for settling a discussion on some basic concepts that arise unavoidably in a formalism that crosses the frontiers of the local-equilibrium theory. Extended irreversible thermodynamics is not at all in conflict with the classical theory of non-equilibrium thermodynamics and rational thermodynamics but must be viewed as a relevant extension of the scope of these descriptions. For the student or the researcher, it may be stimulating to go beyond the classical theories and to enter a of new ideas, new applications, and new problems.

This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respect to macroscopic fluxes or thermodynamic forces. Both irreversible Boltzmann and generalized Boltzmann equations are used for deriving theories of irreversible transport equations and generalized hydrodynamic equations, which rigorously conform to the tenet. All observables described by the so-formulated theories therefore also strictly obey the tenet.