Chaos and randomness: An equivalence proof of a generalized version of the Shannon entropy and the kolmogorov–sinai entropy for Hamiltonian dynamical systems

Abstract
Chaos is often explained in terms of random behaviour; and having positive Kolmogorov–Sinai entropy (KSE) is taken to be indicative of randomness. Although seemly plausible, the association of positive KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. A common way of justifying this use of the KSE is to draw parallels between the KSE and ShannonÕs information theoretic entropy. However, as it stands this no more than a heuristic point, because no rigorous connection between the KSE and ShannonÕs entropy has been established yet. This paper fills this gap by proving that the KSE of a Hamiltonian dynamical system is equivalent to a generalized version of ShannonÕs information theoretic entropy under certain plausible assumptions. Ó 2005 Elsevier Ltd. All rights reserved.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,719
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Entropy-A Guide for the Perplexed.Roman Frigg & Charlotte Werndl - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press.
The Use of the Information-Theoretic Entropy in Thermodynamics.James Ladyman, Stuart Presnell & Anthony J. Short - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (2):315-324.
The Ergodic Hierarchy, Randomness and Hamiltonian Chaos☆.Joseph Berkovitz, Roman Frigg & Fred Kronz - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (4):661-691.
The Ergodic Hierarchy, Randomness and Hamiltonian Chaos.Joseph Berkovitz, Roman Frigg & Fred Kronz - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (4):661-691.
Added to PP index
2009-01-28

Total downloads
54 ( #100,463 of 2,197,279 )

Recent downloads (6 months)
1 ( #298,964 of 2,197,279 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature