๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Chaos and Coarse Graining in Statistical Mechanics

โœ Scribed by Patrizia Castiglione, Massimo Falcioni, Annick Lesne, Angelo Vulpiani

Book ID
127452052
Publisher
Cambridge University Press
Year
2008
Tongue
English
Weight
1 MB
Edition
illustrated edition
Category
Library
ISBN
0511424299

No coin nor oath required. For personal study only.

โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

The coarse-graining approach to statisti
The coarse-graining approach to statistical mechanics: how blissful is our ignorance?
โœ Katinka Ridderbos ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 129 KB

In this paper I first argue that the objection which is most commonly levelled against the coarse-graining approachFviz. that it introduces an element of subjectivity into what ought to be a purely objective formalismFis ultimately unfounded. I then proceed to argue that two different objections to

Long time coarse grain leads to large de
Long time coarse grain leads to large deviation statistics and statistical mechanics
โœ Hiroshi Shibata ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 198 KB

The long time coarse grain of the observables often shows the large deviation statistics. A reason for this is that the long time coarse grained observables lose their correlations or memories. The establishment of the large deviation statistics leads to the statistical mechanics. In this paper, we