The world according to Renyi: Thermodynamics of multifractal systems

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dc.creatorJizba, Petr
dc.creatorArimitsu, Toshihico
dc.date2002-07-30
dc.date2003-12-26
dc.date.accessioned2026-07-07T02:46:37Z
dc.date.available2026-07-07T02:46:37Z
dc.descriptionWe 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 issue for 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 on multifractals. 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.
dc.description24 pages, 2 figures, RevTex, thoroughly revised, accepted to Annals of Physics
dc.identifierhttps://arxiv.org/abs/cond-mat/0207707
dc.identifierhttp://arxiv.org/abs/cond-mat/0207707
dc.identifierAnnals Phys. 312 (2004) 17-57
dc.identifierdoi:10.1016/j.aop.2004.01.002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/19698
dc.subjectStatistical Mechanics
dc.subjectAstrophysics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectData Analysis, Statistics and Probability
dc.titleThe world according to Renyi: Thermodynamics of multifractal systems
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