Detail publikačního výsledku
Entropy of fractal systems
ZMEŠKAL, O.
Original Title
Entropy of fractal systems
English Title
Entropy of fractal systems
Type
Peer-reviewed article not indexed in WoS or Scopus
Original Abstract
The Kolmogorov entropy is an important measure which describes the degree of chaoticity of systems. It gives the average rate of information loss about a position of the phase point on the attractor. Numerically, the Kolmogorov entropy can be estimated as the Rényi entropy. A special case of Rényi entropy is the information theory of Shannon entropy. The product of Shannon entropy and Boltzmann constant is the thermodynamic entropy. Fractal structures are characterized by their fractal dimension. There exists an infinite family of fractal dimensions. A generalized fractal dimension can be defined in an E-dimensional space. The Rényi entropy and generalized fractal dimension are connected by known relation.
English abstract
The Kolmogorov entropy is an important measure which describes the degree of chaoticity of systems. It gives the average rate of information loss about a position of the phase point on the attractor. Numerically, the Kolmogorov entropy can be estimated as the Rényi entropy. A special case of Rényi entropy is the information theory of Shannon entropy. The product of Shannon entropy and Boltzmann constant is the thermodynamic entropy. Fractal structures are characterized by their fractal dimension. There exists an infinite family of fractal dimensions. A generalized fractal dimension can be defined in an E-dimensional space. The Rényi entropy and generalized fractal dimension are connected by known relation.
Keywords
Fractal physics, Fractal geometry, Fractal dimension, Fractal measure, Kolmogorov entropy, Rényi entropy, Shannon entropy, Thermodynamic entropy
Key words in English
Fractal physics, Fractal geometry, Fractal dimension, Fractal measure, Kolmogorov entropy, Rényi entropy, Shannon entropy, Thermodynamic entropy
Authors
ZMEŠKAL, O.
RIV year
2013
Released
03.09.2012
Publisher
Springer
Location
New York, USA
ISBN
2194-5357
Periodical
Advances in Intelligent Systems and Computing
Volume
192
Number
1
State
Swiss Confederation
Pages from
25
Pages to
26
Pages count
2
Full text in the Digital Library
BibTex
@article{BUT93924,
author="Oldřich {Zmeškal}",
title="Entropy of fractal systems",
journal="Advances in Intelligent Systems and Computing",
year="2012",
volume="192",
number="1",
pages="25--26",
issn="2194-5357"
}