Return distributions in dog-flea model revisited

Details Return distributions in dog-flea model revisited Return distributions in dog-flea model revisited

2010-03-29

arxiv.org/abs/1003.5540v2

Physica A 389, 3382 (2010)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 4 eps figures and 1 bbl file, accepted for publication on Physica A, in press (2010)

Scientific paper

10.1016/j.physa.2010.04.037

A recent study of coherent noise model for the system size independent case provides an exact relation between the exponent $\tau$ of avalanche size distribution and the $q$ value of appropriate $q$-Gaussian that fits the return distribution of the model. This relation is applied to Ehrenfest's historical dog-flea model by treating the fluctuations around the thermal equilibrium as avalanches. We provide a clear numerical evidence that the relation between the exponent $\tau$ of fluctuation length distribution and the $q$ value of appropriate $q$-Gaussian obeys this exact relation when the system size is large enough. This allows us to determine the value of $q$-parameter \emph{a priori} from one of the well known exponents of such dynamical systems. Furthermore, it is shown that the return distribution in dog-flea model gradually approaches to $q$-Gaussian as the system size increases and this tendency can be analyzed by a well defined analytical expression.

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