Statistical Mechanics Of Non Equilibrium Processes In Plasmas And Gases

The turbulent equations for a neutral fluid are derived from the standpoint of Statistical Mechanics. The Three-Point Method of turbulence was investigated for limitations on the theory. Turbulent equations applicable to the adiabatic response of a plasma are developed.

A unified approach to the modern statistical theory of nonequilibrium processes. This book explores applications of this unified approach to classical and quantum kinetic theory of nonideal gases, to plasmas, and to solid state physics.

The Statistical Theory of Non-equilibrium Processes in a Plasma covers the modern statistical theory of non-equilibrium processes in a plasma by a unified method, proceeding from the microscopic equations. The book discusses Maxwell equations for slow and fast processes; magnetohydrodynamic equations; microscopic equations for a plasma; and equations with a self-consistent field (Vlasov equations). The text then describes correlation and spectral function; kinetic equations for a plasma; and Landau equations. It also examines the kinetic equations and expressions for spectral functions when the radiation by plasma waves is taken into account; and the hydrodynamic description of processes in a plasma. Physicists and students taking courses in mechanics and mathematics will find the book invaluable.

This book deals with the physics of low temperature plasmas of atomic and molecular gases. Several diagnostic methods for nonequilibrium plasma are described. The relevant elementary processes governing the kinetics and transport of atomic and chemically active molecular plasmas are discussed and numerical models of plasmas aimed at systematically solving MHD-equations are also presented. Intended for use by scientists and engineers active in various fields of low-temperature plasma physics, this book is also suitable for teachers and students at pre- and postgraduate level. In chapter 1 general problems of the elementary physics of plasma are considered and the principal ideas relating to plasma properties are given. In chapter 2 the principles which form the basis of atomic and molecular spectra radiated by a plasma are briefly described. Chapter 3 reviews experimental material associated with the peculiarities of molecular excitation processes in nonequilibrium low-temperature plasma. In chapter 4 a number of problems related to the technique and methods of spectroscopy are considered. Chapter 5 presents experimental material gained from studying the peculiarities of molecular excitation spectra from low-pressure gas discharges and describes diagnostics for nonequilibrium chemically active plasma. In chapter 6 the problems of mathematical modeling of equilibrium plasma in arcs, microwave and optical discharges are analyzed. In chapter 7, a theoretical description of nonequilibrium plasma in electrical arcs, microwave and radio-frequency discharges based on two-temperature approximation of the plasma parameters is offered. Chapter 8 presents a detailed case-study on the transport and excitation of a magnetized plasma of intermediate electron density. Several diagnostic techniques and models introduced in earlier chapters are used to obtain information on plasma properties.

This book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round.

The research covered by the present report ranges over a large variety of topics. The introduction of a quasi-particle description has been shown to lead to a great formal simplification of the generalized kinetic equations, and of the expression for the non-equilibrium entropy; specific systems studied include anharmonic solids, classical gases, plasmas and many-fermion systems. The general relation between the equilibrium Gibbs definition and the non-equilibrium Boltzmann definition of entropy has been elucidated, and the resulting picture departs quite radically from the disorder or information theory image of entropy. The study of gravitational systems has led to a new type of long time evolution equation with interesting properties. The theory of unstable plasmas has been extended to the inhomogeneous case, and to situations with an external magnetic field. Further progress in plasma physics bears on the study of the generalized dielectric constant and of Cerenkov radiation. The hydrodynamical equations for a relativistic system have been derived from a statistical description, and exhibit novel features. Of particular significance is the progress achieved in setting up a covariant formulation of relativistic statistical mechanics. Finally the thermodynamical theory of the local potential has been applied to the study of the Soret effect, and has been extended to include the stability analysis of simple kinetic equations. (Author).

Statistical mechanics provides a framework for relating the properties of macroscopic systems (large collections of atoms, such as in a solid) to the microscopic properties of its parts. However, what happens when macroscopic systems are not in thermal equilibrium, where time is not only a relevant variable, but also essential? That is the province of nonequilibrium statistical mechanics – there are many ways for systems to be out of equilibrium! The subject is governed by fewer general principles than equilibrium statistical mechanics and consists of a number of different approaches for describing nonequilibrium systems. Financial markets are analyzed using methods of nonequilibrium statistical physics, such as the Fokker-Planck equation. Any system of sufficient complexity can be analyzed using the methods of nonequilibrium statistical mechanics. The Boltzmann equation is used frequently in the analysis of systems out of thermal equilibrium, from electron transport in semiconductors to modeling the early Universe following the Big Bang. This book provides an accessible yet very thorough introduction to nonequilibrium statistical mechanics, building on the author's years of teaching experience. Covering a broad range of advanced, extension topics, it can be used to support advanced courses on statistical mechanics, or as a supplementary text for core courses in this field. Key Features: Features a clear, accessible writing style which enables the author to take a sophisticated approach to the subject, but in a way that is suitable for advanced undergraduate students and above Presents foundations of probability theory and stochastic processes and treats principles and basic methods of kinetic theory and time correlation functions Accompanied by separate volumes on thermodynamics and equilibrium statistical mechanics, which can be used in conjunction with this book

This book addresses research challenges in the rapidly developing area of nonequilibrium thermodynamics and fluctuation kinetics. This cross-disciplinary field comprises various topics, ranging from fundamental problems of nonequilibrium statistical mechanics and thermodynamics to multiple applications in plasma, fluid mechanics, nonlinear science, systems of dissipative particles, and high-Q resonators. The purpose of this book is to bring together world-leading experts in the above fields to initiate a cross-fertilization among these active research areas. The book is dedicated to and honours the memory of Professor Slava Belyi who passed away unexpectedly on May 20, 2020. He was pioneering the theory of nonequilibrium fluctuations, in particular the application of the Callen-Welton fluctuation-dissipation theorem to nonequilibrium systems and its generalization. This and related problems also feature in the book.

Written for graduate or advanced students as well as for professionals in physics and chemistry, this book includes the fundamental concepts of statistical physics and physical kinetics. These concepts relate to a wide range of physical objects, such as liquids and solids, gases and plasmas, clusters and systems of complex molecules. The book analyzes various structures of many-particle systems, such as crystal structures, lamellar structures, fractal aggregates and fractal structures, while comparing different methods of description for certain systems and phenomena. Developed from a lecture course on statistical physics and kinetic theory of various atomic systems, the text provides a maximum number of concepts in the simplest way, based on simple problems and using various methods.