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Novel results which reveal phase transition processes in the solar windplasma during shock events are presented in this study which is the first partof a trilogy concerning the solar wind complexity. Solar wind plasma is atypical case of stochastic spatiotemporal distribution of physical magnitudessuch as force fields (B, E) and matter fields (particle and current densitiesor bulk plasma distributions). The results of this study can be understood inthe framework of modern theoretical concepts such as non-extensive statisticalmechanics (Tsallis, 2009), fractal topology (Zelenyi and Milovanov, 2004),turbulence theory (Frisch,1996), strange dynamics (Zaslavsky, 2002),percolation theory (Milovanov, 1997), anomalous diffusion theory and anomaloustransport theory (Milovanov, 2001), fractional dynamics (Tarasov, 2007) andnon-equilibrium phase transition theory (Chang, 1992). This study shows clearlythe non-extensive and non-Gaussian character of the solar wind plasma and theexistence of multi-scale strong correlations from the microscopic to themacroscopic level. This result indicates the inefficiency of classical MHD orplasma statistical theories based on the classical central limit theorem toexplain the complexity of the solar wind dynamics, since these theories includesmooth and differentiable spatial-temporal functions (MHD theory) or Gaussianstatistics (Boltzmann-Maxwell statistical mechanics). However, the results ofthis study indicate the presence of non-Gaussian non-extensive statistics withheavy tails probability distribution functions, which are related to theq-extension of central limit theorem.

Studying Complexity in Solar Wind Plasma During Shock Events. Part I: Nonextensive Tsallis Statistics