  Novel results which reveal phase transition processes in the solar wind
plasma during shock events are presented in this study which is the first part
of a trilogy concerning the solar wind complexity. Solar wind plasma is a
typical case of stochastic spatiotemporal distribution of physical magnitudes
such as force fields (B, E) and matter fields (particle and current densities
or bulk plasma distributions). 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, 2007) and
non-equilibrium phase transition theory (Chang, 1992). 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. This result indicates the inefficiency of classical MHD or
plasma statistical theories based on the classical central limit theorem 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). However, 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
q-extension of central limit theorem.
