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Title Multifractal spectrum of phase space related to generalized thermostatistics
Authors Oliemskoi, Oleksandr Ivanovych
Kharchenko, V.O.
Borysiuk, Vadym Mykolaiovych
ORCID
Keywords phase space
multifractal spectrum
statistical weight
Type Article
Date of Issue 2008
URI http://essuir.sumdu.edu.ua/handle/123456789/2755
Publisher Physica A
License
Citation Olemskoy, A.I. Multifractal spectrum of phase space related to generalized thermostatistics [Текст] / A.I. Olemskoy, V.O. Kharchenko, V.N. Borisyuk // Physica A. — 2008. — vol.387. — p. 1895-1906
Abstract We consider a self-similar phase space with specific fractal dimension d being distributed with spectrum function f(d). Related thermostatistics is shown to be governed by the Tsallis formalism of the non-extensive statistics,where the non-additivity parameter equals to τ(q)≡1/τ(q)> 1, and the multifractal function τ(q)=qdq−f(dq ) is the specific heat determined with multifractal parameter q є [1,∞]. At that,the equipartition law is shown to take place. Optimization of the multifractal spectrum function f(d) arrives at the relation between the statistical weight and the system complexity. It is shown that the statistical weight exponent τ(q) can be modeled by hyperbolic tangent deformed in accordance with both Tsallis and Kaniadakis exponential functions to describe arbitrary multifractal phase space explicitly. The spectrum function f(d) is proved to increase monotonically from minimum value f=-1 at d=0 to maximum one f=1 at d=1. At the same time, the number of monofractals increases with the growth of the phase-space volume at small dimensions d and falls down in the limit d->1. При цитуванні документа, використовуйте посилання http://essuir.sumdu.edu.ua/handle/123456789/2755
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