Hard Ball Systems and the Lorentz Gas
Hard Ball Systems and the Lorentz Gas

Author: D. Szasz

Publisher: Springer Science & Business Media

Published: 2013-12-11

Total Pages: 458

ISBN-13: 366204062X

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Hard Ball Systems and the Lorentz Gas are fundamental models arising in the theory of Hamiltonian dynamical systems. Moreover, in these models, some key laws of statistical physics can also be tested or even established by mathematically rigorous tools. The mathematical methods are most beautiful but sometimes quite involved. This collection of surveys written by leading researchers of the fields - mathematicians, physicists or mathematical physicists - treat both mathematically rigourous results, and evolving physical theories where the methods are analytic or computational. Some basic topics: hyperbolicity and ergodicity, correlation decay, Lyapunov exponents, Kolmogorov-Sinai entropy, entropy production, irreversibility. This collection is a unique introduction into the subject for graduate students, postdocs or researchers - in both mathematics and physics - who want to start working in the field.

Contemporary Kinetic Theory of Matter
Contemporary Kinetic Theory of Matter

Author: J. R. Dorfman

Publisher: Cambridge University Press

Published: 2021-06-24

Total Pages: 667

ISBN-13: 1009038222

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Kinetic theory provides a microscopic description of many observable, macroscopic processes and has a wide range of important applications in physics, astronomy, chemistry, and engineering. This powerful, theoretical framework allows a quantitative treatment of many non-equilibrium phenomena such as transport processes in classical and quantum fluids. This book describes in detail the Boltzmann equation theory, obtained in both traditional and modern ways. Applications and generalizations describing non-equilibrium processes in a variety of systems are also covered, including dilute and moderately dense gases, particles in random media, hard sphere crystals, condensed Bose-Einstein gases, and granular materials. Fluctuation phenomena in non-equilibrium fluids, and related non-analyticities in the hydrodynamic equations are also discussed in some detail. A thorough examination of many topics concerning time dependent phenomena in material systems, this book describes both current knowledge as well as future directions of the field.

Advances in Chemical Physics, Volume 58
Advances in Chemical Physics, Volume 58

Author: Ilya Prigogine

Publisher: John Wiley & Sons

Published: 2009-09-08

Total Pages: 393

ISBN-13: 0470143274

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The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

From Particle Systems to Partial Differential Equations II
From Particle Systems to Partial Differential Equations II

Author: Patrícia Gonçalves

Publisher: Springer

Published: 2015-04-04

Total Pages: 395

ISBN-13: 3319166379

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This book focuses on mathematical problems concerning different applications in physics, engineering, chemistry and biology. It covers topics ranging from interacting particle systems to partial differential equations (PDEs), statistical mechanics and dynamical systems. The purpose of the second meeting on Particle Systems and PDEs was to bring together renowned researchers working actively in the respective fields, to discuss their topics of expertise and to present recent scientific results in both areas. Further, the meeting was intended to present the subject of interacting particle systems, its roots in and impacts on the field of physics and its relation with PDEs to a vast and varied public, including young researchers. The book also includes the notes from two mini-courses presented at the conference, allowing readers who are less familiar with these areas of mathematics to more easily approach them. The contributions will be of interest to mathematicians, theoretical physicists and other researchers interested in interacting particle systems, partial differential equations, statistical mechanics, stochastic processes, kinetic theory, dynamical systems and mathematical modeling aspects.

Microscopic Chaos, Fractals And Transport In Nonequilibrium Statistical Mechanics
Microscopic Chaos, Fractals And Transport In Nonequilibrium Statistical Mechanics

Author: Rainer Klages

Publisher: World Scientific

Published: 2007-06-15

Total Pages: 458

ISBN-13: 9814479314

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A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory.Understanding macroscopic properties of matter starting from microscopic chaos in the equations of motion of single atoms or molecules is a key problem in nonequilibrium statistical mechanics. Of particular interest both for theory and applications are transport processes such as diffusion, reaction, conduction and viscosity.Recent advances towards a deterministic theory of nonequilibrium statistical physics are summarized: Both Hamiltonian dynamical systems under nonequilibrium boundary conditions and non-Hamiltonian modelings of nonequilibrium steady states by using thermal reservoirs are considered. The surprising new results include transport coefficients that are fractal functions of control parameters, fundamental relations between transport coefficients and chaos quantities, and an understanding of nonequilibrium entropy production in terms of fractal measures and attractors.The theory is particularly useful for the description of many-particle systems with properties in-between conventional thermodynamics and nonlinear science, as they are frequently encountered on nanoscales.

Introduction to Plasma Physics
Introduction to Plasma Physics

Author: D. A. Gurnett

Publisher: Cambridge University Press

Published: 2005-01-06

Total Pages: 468

ISBN-13: 9780521364836

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Advanced undergraduate/beginning graduate text on space and laboratory plasma physics.