Return distributions in dog-flea model revisited

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