The world according to R enyi: thermodynamics of multifractal systems
By Petr Jizba, T. Arimitsu. 2002
261 citations recorded by the source corpus.
We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs–Shannon entropy into more general framework—R enyi s information entropy. We address the renormalization issue for R enyi s entropy on (multi)fractal sets and consequently show how R enyi s parameter is connected with multifractal singularity spectrum. The maximal entropy approach then provides a passage between R enyi s information entropy and thermodynamics of multifractals. Important issues such as R enyi s entropy versus Tsallis–Havrda–Charvat entropy and PDF reconstruction theorem are also studied. Finally, some further speculations on a possible relevance of our approach to cosmology are discussed. 2004 Elsevier Inc. All rights reserved. PACS: 65.40.Gr; 47.53.+n; 05.90.+m
Subfields: Molecular Biology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/aa138057212166768de682e9828ab8625ed3c23e
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In Molecular Biology
In Statistical and Nonlinear Physics
Citations in the corpus
- On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles (2006, methodology): “We notice that a similar generalization exists for the Tsallis entropy [18,19,20], which is widely used in statistical physics and related to the Rényi entropy by an invertible transformation [10,11,12,21,22].”
- A step beyond Tsallis and Rényi entropies (2005, background): “Arimitsu (5) showed that Rényi’s measure can be obtained also extending the Shannon-Khinchin axioms to a quasi-linear conditional information”
- Thermodynamics (2021, unknown): “These are constructed by choosing 2 N random vector components c n from a symmetric probability distribution ([32]) to form the infinite-temperature states It is essential that the vector components are uncorrelated.”