A nonextensive entropy path to probability distributions in solar wind turbulence

The observed scale dependence of the probability distributions of the differences of characteristic solar wind variables is analyzed. Intermittency of the turbulent fluctuations at small-scale spatial separations is accompanied by strongly non-Gaussian distributions that turn into a normal distribution for large-scale separation. Conventional theoretical models are subject to insufficient physical justification since nonlocality in turbulence should be based on long-range interactions, provided recently by the bi-kappa distribution in the context of nonextensive thermostatistics. Observed WIND and ACE probability distributions are accurately reproduced for different time lags by the one-parameter bi-kappa functional, a core-halo convolution, where kappa measures the degree of nonlocality or nonextensivity in the system. Gradual decoupling is obtained by enhancing the spatial separation scale corresponding to increasing kappa values, where a Gaussian is approached for infinite kappa. Consequently, long-range interactions introduced on the fundamental level of entropy generalization, are able to provide physically the source of the observed scale dependence of the turbulent fluctuations in the intermittent interplanetary medium.