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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 | Copyright not evaluated |
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.
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Multifractal spectrum of phase space related to generalized thermostatistics.pdf | 829.87 kB | Adobe PDF | -1821714583 |
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