Many-body theory stands at the foundation of modern quantum statistical mechanics. It is introduced here to graduate students in physics, chemistry, engineering and biology. The book provides a contemporary understanding of irreversibility, particularly in quantum systems. It explains entropy production in quantum kinetic theory and in the master equation formulation of non-equilibrium statistical mechanics. The first half of the book focuses on the foundations of non-equilibrium statistical mechanics with emphasis on quantum mechanics. The second half of the book contains alternative views of quantum statistical mechanics, and topics of current interest for advanced graduate level study and research. Unique to textbooks on this subject, this book contains a discussion of the fundamental Gleason theorem. Quantum entanglements are treated in application to quantum computation and the difficulties arising from decoherence. The relativistic generalization of the Boltzmann equation is derived, and modern transport applications to reservoir ballistic transport are developed.

Twentieth-century research in the field of chemical pattern formation saw extraordinary progress due to the pathbreaking contributions of Nobel laureate Ilya Prigogine and his co-workers. Evidence exists that the dissipative structures studied by Prigogine and his colleagues may play a dominant role in the processes of self-organization of biological systems, the fundamental phenomena that govern all life forms. Brought together in this valuable volume are topical papers from the this research. Important aspects of nonlinear chemical pattern formation-dissipative structures-in chemical, biochemical, and geological systems are surveyed by leading scientists in the field of nonlinear chemistry. Topics covered include experimental observations of pattern formation in a variety of systems, bifurcation theory and analysis of nonlinear chemical rate equations, and the stochastic theory of nonlinear chemical reactions. Of particular interest are the studies of the effects of electric fields on the determination of nonequilibrium states of chemical systems.

The contributions to this volume attempt to apply different aspects of Ilya Prigogine's Nobel-prize-winning work on dissipative structures to nonchemical systems as a way of linking the natural and social sciences. They address both the mathematical methods for description of pattern and form as they evolve in biological systems and the mechanisms of the evolution of social systems, containing many variables responding to subjective, qualitative stimuli. The mathematical modeling of human systems, especially those far from thermodynamic equilibrium, must involve both chance and determinism, aspects both quantitative and qualitative. Such systems (and the physical states of matter which they resemble) are referred to as self-organized or dissipative structures in order to emphasize their dependence on the flows of matter and energy to and from their surroundings. Some such systems evolve along lines of inevitable change, but there occur instances of choice, or bifurcation, when chance is an important factor in the qualitative modification of structure. Such systems suggest that evolution is not a system moving toward equilibrium but instead is one which most aptly evokes the patterns of the living world. The volume is truly interdisciplinary and should appeal to researchers in both the physical and social sciences. Based on a workshop on dissipative structures held in 1978 at the University of Texas, contributors include Prigogine, A. G. Wilson, Andre de Palma, D. Kahn, J. L. Deneubourgh, J. W. Stucki, Richard N. Adams, and Erick Jantsch. The papers presented include Allen, "Self-Organization in the Urban System"; Robert Herman, "Remarks on Traffic Flow Theories and the Characterization of Traffic in Cities"; W. H. Zurek and Schieve, "Nucleation Paradigm: Survival Threshold in Population Dynamics"; De Palma et al., "Boolean Equations with Temporal Delays"; Nicholas Georgescu-Roegin, "Energy Analysis and Technology Assessment"; Magoroh Maruyama, "Four Different Causal Meta-types in Biological and Social Sciences"; and Jantsch, "From Self-Reference to Self-Transcendence: The Evolution of Self-Organization Dynamics."