Chaos and Coarse Graining in Statistical Mechanics

Erscheinungsjahr 2008
ISBN: 978-0-521-89593-4
Verlag: Cambridge University Press

Buch, Englisch, 280 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 667 g

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.

Autoren/Hrsg.

Castiglione, Patrizia

Falcioni, Massimo

Lesne, Annick

Vulpiani, Angelo

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

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.

Über Autor(innen)

Lesne, Annick
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.

Castiglione, Patrizia
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.

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

Vulpiani, Angelo
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.