Tsallis non-extensive statistics and solar wind plasma complexity

•The qq-statistics of Tsallis theory in solar wind plasma dynamics is verified both in calm and shock periods.•Non-equilibrium phase transitions are verified in solar wind plasma dynamics during calm and shock periods.•Agreement of predictions of Tsallis theory and experimental estimations, concerning multifractality.•Theoretical extensions of qq-statistics of Tsallis statistics for renormalization processes.•Fractional dynamics and solar wind plasma.

This article presents novel results revealing non-equilibrium phase transition processes in the solar wind plasma during a strong shock event, which took place on 26th September 2011. Solar wind plasma is a typical case of stochastic spatiotemporal distribution of physical state variables such as force fields (B→,E→) and matter fields (particle and current densities or bulk plasma distributions). This study shows clearly the non-extensive and non-Gaussian character of the solar wind plasma and the existence of multi-scale strong correlations from the microscopic to the macroscopic level. It also underlines the inefficiency of classical magneto–hydro-dynamic (MHD) or plasma statistical theories, based on the classical central limit theorem (CLT), to explain the complexity of the solar wind dynamics, since these theories include smooth and differentiable spatial–temporal functions (MHD theory) or Gaussian statistics (Boltzmann–Maxwell statistical mechanics). On the contrary, the results of this study indicate the presence of non-Gaussian non-extensive statistics with heavy tails probability distribution functions, which are related to the qq-extension of CLT. Finally, the results of this study can be understood in the framework of modern theoretical concepts such as non-extensive statistical mechanics (Tsallis, 2009), fractal topology (Zelenyi and Milovanov, 2004), turbulence theory (Frisch, 1996), strange dynamics (Zaslavsky, 2002), percolation theory (Milovanov, 1997), anomalous diffusion theory and anomalous transport theory (Milovanov, 2001), fractional dynamics (Tarasov, 2013) and non-equilibrium phase transition theory (Chang, 1992).