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Return distributions in dog-flea model revisited

Author

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  • Bakar, Burhan
  • Tirnakli, Ugur

Abstract

A recent study of coherent noise model for the system size independent case provides an exact relation between the exponent τ of avalanche size distribution and the q value of the 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 τ of fluctuation length distribution and the q value of the appropriate q-Gaussian obeys this exact relation when the system size is large enough. This allows us to determine the value of the q-parameter 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 q-Gaussian as the system size increases and this tendency can be analyzed by a well defined analytical expression.

Suggested Citation

  • Bakar, Burhan & Tirnakli, Ugur, 2010. "Return distributions in dog-flea model revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3382-3386.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:17:p:3382-3386
    DOI: 10.1016/j.physa.2010.04.037
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