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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.
This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statistical mechanics. This will interest specialists of various fields, especially the (classical and quantum) plasma physics. However, quantum physics — to which a major part is devoted — will be of more interest since, not only it applies to quantum plasma physics, but also to nuclear matter and to strong magnetic field, cosmology, etc. Although the domain of gauge theory is not covered in this book, the topic is not completely forgotten, in particular in the domain of plasma physics. This book is particularly readable for graduate students and a fortiori to young researchers for whom it offers methods and also appropriate schemes to deal with the current problems encountered in astrophysics, in strong magnetic, in nuclear or even in high energy physics.
This 2008 book, reissued as OA, captures the essence of nonequilibrium quantum field theory, graduate students and researchers.
Interpreting general relativity relies on a proper description of non-inertial frames and Dirac observables. This book describes global non-inertial frames in special and general relativity. The first part covers special relativity and Minkowski space time, before covering general relativity, globally hyperbolic Einstein space-time, and the application of the 3+1 splitting method to general relativity. The author uses a Hamiltonian description and the Dirac–Bergmann theory of constraints to show that the transition between one non-inertial frame and another is a gauge transformation, extra variables describing the frame are gauge variables, and the measureable matter quantities are gauge invariant Dirac observables. Point particles, fluids and fields are also discussed, including how to treat the problems of relative times in the description of relativistic bound states, and the problem of relativistic centre of mass. Providing a detailed description of mathematical methods, the book is perfect for theoretical physicists, researchers and students working in special and general relativity.
This book discusses in depth many of the key problems in non-equilibrium physics. The origin of macroscopic irreversible behavior receives particular attention and is illustrated in the framework of solvable models. An updated discussion on the linear response focuses on the correct electrodynamic aspects, which are essential for example, in the proof of the Nyquist theorem. The material covers the scaling relationship between different levels of description (kinetic to hydrodynamic) as well as spontaneous symmetry breaking in real time in terms of nonlinear dynamics (attractors), illustrated using the example of Bose-Einstein condensation. The presentation also includes the latest developments ? quantum kinetics ? related to modern ultrafast spectroscopy, where transition from reversible to irreversible behavior occurs.
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.
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.
This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statistical mechanics. This will interest specialists of various fields, especially the (classical and quantum) plasma physics. However, quantum physics ? to which a major part is devoted ? will be of more interest since, not only it applies to quantum plasma physics, but also to nuclear matter and to strong magnetic field, cosmology, etc. Although the domain of gauge theory is not covered in this book, the topic is not completely forgotten, in particular in the domain of plasma physics. This book is particularly readable for graduate students and a fortiori to young researchers for whom it offers methods and also appropriate schemes to deal with the current problems encountered in astrophysics, in strong magnetic, in nuclear or even in high energy physics.
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.