Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems

Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to power-law statistics are investigated. It is demonstrated that, from a...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2006-09, Vol.74 (3 Pt 2), p.036120-036120, Article 036120
Main Authors: Vakarin, E V, Badiali, J P
Format: Article
Language:English
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Summary:Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to power-law statistics are investigated. It is demonstrated that, from a quite general point of view, the power-law dependencies may appear as a consequence of "global" constraints restricting both the dynamic phase space and the stochastic fluctuations. As a result, at sufficiently long observation times the dynamic counterpart is driven into a nonequilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.74.036120