The world according to Renyi: Thermodynamics of multifractal systems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F04%3A04103199" target="_blank" >RIV/68407700:21340/04:04103199 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
The world according to Renyi: Thermodynamics of multifractal systems
Original language description
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 - Renyi's information entropy. We address the renormalization issuefor Renyi's entropy on (multi)fractal sets and consequently show how Renyi's parameter is connected with multifractal singularity spectrum. The maximal entropy approach then provides a passage between Renyi's information entropy and thermodynamics onmultifractals. Important issues as, for instance, Renyi'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.
Czech name
Svet podle renyiho: termodynamika multifraktalnich systemu
Czech description
Pouzivame Renyiho entropy k analyze multifraktalnich systemu. Diskutujeme otazky tykajici se renormalizace Renyiho entropie na (multi)fraktalnich mnozinach. Vyjasnujeme take roli Renyiho parametru ve fyzikalnich systemech.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Publication year
2004
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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