Chaos and Coarse Graining in Statistical Mechanics

by Patrizia Castiglione, Massimo Falcioni, Annick Lesne, Angelo Vulpiani

Overview

While statistical mechanics describe the equilibrium state of systems with many degrees of freedom, and dynamical systems explain the irregular evolution of systems with few degrees of freedom, new tools are needed to study the evolution of systems with many degrees of freedom. This book presents the basic aspects of chaotic systems, with emphasis on systems composed by huge numbers of particles. Firstly, the basic concepts of chaotic dynamics are introduced, moving on to explore the role of ergodicity and chaos for the validity of statistical laws, and ending with problems characterized by the presence of more than one significant scale. Also discussed is the relevance of many degrees of freedom, coarse graining procedure, and instability mechanisms in justifying a statistical description of macroscopic bodies. Introducing the tools to characterize the non asymptotic behaviors of chaotic systems, this text will interest researchers and graduate students in statistical mechanics and chaos.

Product Details

ISBN-13:	9780521895934
Publisher:	Cambridge University Press
Publication date:	08/21/2008
Pages:	280
Product dimensions:	7.00(w) x 9.80(h) x 0.80(d)

About the Author

Patrizia Castiglione is a Researcher at the Institut des Nanosciences de Paris. Her main research topics are dynamical systems theory, quantum and classic chaos, turbulence, and the physics of colours applied to the study of artwork.

Massimo Falcioni is a Researcher at the University of Rome 'Sapienza'. His research focuses on elementary particle physics, dynamical systems and statistical mechanics.

Annick Lesne is a Researcher at the Institut des Hautes Etudes Scientifiques. Her research lies in renormalization methods for dynamical systems, non equilibrium statistical physics, and applications of dynamical systems theory and statistical mechanics to biological systems.

Angelo Vulpiani is a Professor of Theoretical Physics at the University of Rome “Sapienza”, and is a Fellow of the Institute of Physics. His research interests are statistical mechanics, dynamical systems, turbulence, transport and reaction-diffusion in fluids.

Table of Contents

1. Basic concepts of dynamical systems theory; 2. Dynamical indicators for chaotic systems: Lyapunov exponents, entropies and beyond; 3. Coarse graining, entropies and Lyapunov exponents at work; 4. Foundation of the statistical mechanics and dynamical systems; 5. On the origin of irreversibility; 6. The role of chaos in non-equilibrium statistical mechanics; 7. Coarse-graining equations in complex systems; 8. Renormalization-group approaches; Index.

Editorial Reviews

"This is an excellent book written in highly polished fashion by four experts in the fields of dynamical systems and statistical mechanics."
Irwin Oppenheim, Journal of Statistical Physics

From the Publisher