Universality of First and Second Order Phase Transition in Solar Activity: Evidence for Nonextensive Tsallis Statistics

In this work, we present the coexistence of self-organized criticality (SOC) and low-dimensional chaos at solar activity with results obtained by using the intermittent turbulence theory, the nonextensive q-statistics of Tsallis as well as the singular value decomposition analysis. Particularly, we show the independent dynamics of sunspot system related to the convection zone of sun and the solar flare system related to the lower solar atmosphere. However, both systems reveal nonequilibrium phase transition process from a high-dimensional intermittent turbulence state with SOC profile to a low-dimensional and chaotic intermittent turbulence state. The high-dimensional SOC state in both dynamical systems underlying the sunspot and solar flare signal is related with low q-values and low Flatness values (F ) while the low-dimensional chaotic state is related with higher q-values and Flatness F -values. The higher qand F -values reveal strong character of long-range correlations corresponding to system-wide global process while the lower qand F -values reveal scale invariant local avalanche process. Also, the high-dimensional SOC state corresponds to second order nonequilibrium critical phase transition process while the low-dimensional chaotic state corresponds to first order nonequilibrium phase transition process. Finally, for both dynamics underlying sunspot index and solar flare, at both states of phase transition process, the multiscale and multifractal character was found to exist but with different profile or strength.