All engineering processes are processes of non-equilibrium because one or all of heat, mass, and momentum transfer occur in an open system. The pure equilibrium state can be established in an isolated system, in which neither mass nor heat is transferred between the system and the environment. Most engineering transport analyses are based on the semi-, quasi-, or local equilibrium assumptions, which assume that any infinitesimal volume can be treated as a box of equilibrium. This book includes various aspects of non-equilibrium or irreversible statistical mechanics and their relationships with engineering applications. I hope that this book contributes to expanding the predictability of holistic engineering consisting of thermo-, fluid, and particle dynamics.

Topological defects formed at symmetry-breaking phase transitions play an important role in many different fields of physics. They appear in many condensed-matter systems at low temperature; examples include vortices in superfluid helium-4, a rich variety of defects in helium-3, quantized mag netic flux tubes in type-II superconductors, and disclination lines and other defects in liquid crystals. In cosmology, unified gauge theories of particle interactions suggest a sequence of phase transitions in the very early uni verse some of which may lead to defect formation. In astrophysics, defects play an important role in the dynamics of neutron stars. In 1997 the European Science Foundation started the scientific network "Topological defects" headed by Tom Kibble. This network has provided us with a unique opportunity of establishing a collaboration between the representatives of these very different branches of modern physics. The NATO-ASI (Advanced Study Institute), held in Les Houches in February 1999 thanks to the support of the Scientific Division of NATO, the European Science Foundation and the CNRS, represents a key event of this ESF network. It brought together participants from widely different fields, with diverse expertise and vocabulary, fostering the exchange of ideas. The lectures given by particle physicists, cosmologists and condensed matter physicists are the result of the fruitful collaborations established since 1997 between groups in several European countries and in the U.S.A.

This coherent collection of theory, algorithms, and illustrative results presents the field of nonequilibrium molecular dynamics in detail.

7.1 Introduction -- 7.2 Rotational Energy Exchange Models -- 7.2.1 Constant Collision Number -- 7.2.2 The Parker Model -- 7.2.3 Variable Probability Exchange Model of Boyd -- 7.2.4 Nonequilibrium Direction Dependent Model -- 7.2.5 Model Results -- 7.3 Vibrational Energy Exchange Models -- 7.3.1 Constant Collision Number -- 7.3.2 The Millikan-White Model -- 7.3.3 Quantized Treatment for Vibration -- 7.3.4 Model Results -- 7.4 Dissociation Chemical Reactions -- 7.4.1 Total Collision Energy Model -- 7.4.2 Redistribution of Energy Following a Dissociation Reaction -- 7.4.3 Vibrationally Favored Dissociation Model -- 7.5 General Chemical Reactions -- 7.5.1 Reaction Rates and Equilibrium Constant -- 7.5.2 Backward Reaction Rates in DSMC -- 7.5.3 Three-Body Recombination Reactions -- 7.5.4 Post-Reaction Energy Redistribution and General Implementation -- 7.5.5 DSMC Solutions for Reacting Flows -- 7.6 Summary -- Appendix A: Generating Particle Properties -- Appendix B: Collisional Quantities -- Appendix C: Determining Post-Collision Velocities -- Appendix D: Macroscopic Properties -- Appendix E: Common Integrals -- References -- Index

Recent years have witnessed a resurgence in the kinetic approach to dynamic many-body problems. Modern kinetic theory offers a unifying theoretical framework within which a great variety of seemingly unrelated systems can be explored in a coherent way. Kinetic methods are currently being applied in such areas as the dynamics of colloidal suspensions, granular material flow, electron transport in mesoscopic systems, the calculation of Lyapunov exponents and other properties of classical many-body systems characterised by chaotic behaviour. The present work focuses on Brownian motion, dynamical systems, granular flows, and quantum kinetic theory.

This book offers a self-contained introduction to non-equilibrium quantum particle dynamics for inhomogeneous systems, including a survey of recent breakthroughs pioneered by the authors and others. The approach is based on real-time Green’s functions.

As our title suggests, there are two aspects in the subject of this book. The first is the mathematical investigation of the dynamics of infinite systems of in teracting particles and the description of the time evolution of their states. The second is the rigorous derivation of kinetic equations starting from the results of the aforementioned investigation. As is well known, statistical mechanics started in the last century with some papers written by Maxwell and Boltzmann. Although some of their statements seemed statistically obvious, we must prove that they do not contradict what me chanics predicts. In some cases, in particular for equilibrium states, it turns out that mechanics easily provides the required justification. However things are not so easy, if we take a step forward and consider a gas is not in equilibrium, as is, e.g., the case for air around a flying vehicle. Questions of this kind have been asked since the dawn of the kinetic theory of gases, especially when certain results appeared to lead to paradoxical conclu sions. Today this matter is rather well understood and a rigorous kinetic theory is emerging. The importance of these developments stems not only from the need of providing a careful foundation of such a basic physical theory, but also to exhibit a prototype of a mathematical construct central to the theory of non-equilibrium phenomena of macroscopic size.