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Strong evidence is provided for significant far from equilibrium complex processes in the seismogenic layer of the North Aegean region (Greece), after applying modern nonlinear methods to various seismicity time series. The data used are subsets of the regional catalogue compiled in the central Seismological Station of Geophysics Department, Aristotle University of Thessaloniki and concern 4367 earthquakes of magnitude greater than 3.8, which took place during the period of 1968-2008. We present results, derived from the application of nonlinear algorithms, concerning the estimation of correlation dimension, mutual information, largest Lyapunov exponent, flatness coefficient and q-value which correspond to Tsallis nonextensive statistics. These quantities are estimated for two seismic time series corresponding to the basic focal parameters of earthquakes, namely origin time and magnitude. The obtained results can be associated with novel far from equilibrium complex dynamics such as low dimensional chaos, Self Organized Criticality (SOC) and intermittent turbulence. Furthermore, in this study, new information is provided about the nonlinear turbulent character of the Hellenic lithospheric dynamics related to the Tsallis nonextensive statistical theory. Our analysis indicates the coexistence of two different lithospheric processes, one low dimensional (chaotic) and the other high dimensional (SOC), revealing the strongly turbulent character of the Greek lithospheric system. In particular, the low dimensional chaotic process corresponds to the temporal manifestation of earthquakes, whereas the high dimensional nonlinear (SOC) process corresponds to the burst energy releases, a result that has significant implications concerning the ability of earthquake prediction. [ABSTRACT FROM AUTHOR]