This book describes recent advances in the application of chaos theory to classical scattering and nonequilibrium statistical mechanics generally, and to transport by deterministic diffusion in particular. The author presents the basic tools of dynamical systems theory, such as dynamical instability, topological analysis, periodic-orbit methods, Liouvillian dynamics, dynamical randomness and large-deviation formalism. These tools are applied to chaotic scattering and to transport in systems near equilibrium and maintained out of equilibrium. This book will be bought by researchers interested in chaos, dynamical systems, chaotic scattering, and statistical mechanics in theoretical, computational and mathematical physics and also in theoretical chemistry.
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Book Description
Editorial Reviews
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"...gives both the background and an overview of recent developments in nonequilibrium statistical mechanics, to which the author himself has made major contributions...an important reference book as well as an ideal tool for advanced students in the expanding and important field of statistical physics." Physics Today
"The book is nicely written...allows one to see some topics in dynamical systems with new eyes." Mathematical Reviews
"The book is nicely written...allows one to see some topics in dynamical systems with new eyes." Mathematical Reviews
Book Description
This book describes new results at the frontier of chaos theory applied to nonequilibrium statistical mechanics and to chaotic scattering. Interest in the results of studies of the foundations of statistical mechanics from the viewpoint of chaos theory has been growing worldwide. The author describes how to characterize chaos and sensitivity to initial conditions, especially in Hamiltonian systems and billiards. These methods are then applied to scattering and reaction processes as well as to transport such as diffusion or viscosity as studied in nonequilibrium statistical mechanics, or the 2nd law of thermodynamics.
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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First Sentence:
The time evolution of many natural systems is ruled by ordinary differential equations which are autonomous if there is no time-dependent forcing. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
forward semigroup, topological zeta function, multibaker map, dynamical randomness, fundamental periodic orbits, fractal repeller, hyperbolic repeller, local stretching rates, thermostatted systems, prime periodic orbits, backward semigroup, regular randomness, interdisk distance, leading eigenstate, topological transition matrix, inverted harmonic potential, phenomenological diffusion equation, quasiperiodic boundary conditions, ingoing trajectories, microscopic chaos, entropy per unit time, forward time evolution, ingoing trajectory, disk scatterers, nonequilibrium constraints Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
The time evolution of many natural systems is ruled by ordinary differential equations which are autonomous if there is no time-dependent forcing. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
forward semigroup, topological zeta function, multibaker map, dynamical randomness, fundamental periodic orbits, fractal repeller, hyperbolic repeller, local stretching rates, thermostatted systems, prime periodic orbits, backward semigroup, regular randomness, interdisk distance, leading eigenstate, topological transition matrix, inverted harmonic potential, phenomenological diffusion equation, quasiperiodic boundary conditions, ingoing trajectories, microscopic chaos, entropy per unit time, forward time evolution, ingoing trajectory, disk scatterers, nonequilibrium constraints Key Phrases - Capitalized Phrases (CAPs): (learn more)
Van Hove, Selberg-Smale Zeta New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 70
books:
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10
books
cite this book:
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- Microscopic Simulations of Complex Hydrodynamic Phenomena (NATO Science Series B: Physics) by Michel Mareschal in Back Matter (1), and Back Matter (2)
- Directions in Chaos (World Scientific Series on Directions in Condensed Matter Physics) by Hao Bai-Lin in Back Matter (1), and Back Matter (2)
- Directions in Chaos (World Scientific Series on Directions in Condensed Matter Physics) by B. L. Hao in Back Matter (1), and Back Matter (2)
- Ergodic Theory (Grundlehren der mathematischen Wissenschaften) by I. P. Kornfeld in Back Matter (1), and Back Matter (2)
- Equilibrium and Non-Equilibrium Statistical Mechanics by Radu C. Balescu in Back Matter
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- Matter in Equilibrium: Statistical Mechanics and Thermodynamics includes CD-ROM (Topics in Physical Chemistry) by R. Stephen Berry on page 445, and page 473
- Collective Dynamics of Nonlinear and Disordered Systems by Günter Radons on page 298, and page 356
- Quantum Chaos and Quantum Dots (Mesoscopic Physics and Nanotechnology) by Katsuhiro Nakamura in Back Matter
- Chaotic Dynamics and Transport in Classical and Quantum Systems by Pierre Collet on page 154
- Chaotic Dynamics and Transport in Classical and Quantum Systems: Proceedings of the NATO Advanced Study Institute on International Summer School on ... II: Mathematics, Physics and Chemistry) by Pierre Collet on page 154
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