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Title: Fisher information and Rényi dimensions: A thermodynamical formalism

Abstract

The relation between the Fisher information and Rényi dimensions is established: the Fisher information can be expressed as a linear combination of the first and second derivatives of the Rényi dimensions with respect to the Rényi parameter β. The Rényi parameter β is the parameter of the Fisher information. A thermodynamical description based on the Fisher information with β being the inverse temperature is introduced for chaotic systems. The link between the Fisher information and the heat capacity is emphasized, and the Fisher heat capacity is introduced.

Authors:
;  [1]
  1. Department of Theoretical Physics, University of Debrecen, H–4002 Debrecen (Hungary)
Publication Date:
OSTI Identifier:
22596558
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 26; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; CHAOS THEORY; FRACTALS; INFORMATION; SPECIFIC HEAT

Citation Formats

Godó, B., and Nagy, Á. Fisher information and Rényi dimensions: A thermodynamical formalism. United States: N. p., 2016. Web. doi:10.1063/1.4959908.
Godó, B., & Nagy, Á. Fisher information and Rényi dimensions: A thermodynamical formalism. United States. doi:10.1063/1.4959908.
Godó, B., and Nagy, Á. Mon . "Fisher information and Rényi dimensions: A thermodynamical formalism". United States. doi:10.1063/1.4959908.
@article{osti_22596558,
title = {Fisher information and Rényi dimensions: A thermodynamical formalism},
author = {Godó, B. and Nagy, Á.},
abstractNote = {The relation between the Fisher information and Rényi dimensions is established: the Fisher information can be expressed as a linear combination of the first and second derivatives of the Rényi dimensions with respect to the Rényi parameter β. The Rényi parameter β is the parameter of the Fisher information. A thermodynamical description based on the Fisher information with β being the inverse temperature is introduced for chaotic systems. The link between the Fisher information and the heat capacity is emphasized, and the Fisher heat capacity is introduced.},
doi = {10.1063/1.4959908},
journal = {Chaos (Woodbury, N. Y.)},
number = 8,
volume = 26,
place = {United States},
year = {Mon Aug 15 00:00:00 EDT 2016},
month = {Mon Aug 15 00:00:00 EDT 2016}
}