First and second order non-equilibrium phase transition and evidence for non-extensive Tsallis statistics in Earth’s magnetosphere

In this paper strong evidence is provided for significant far from equilibrium phase transition processes in the Earth’s magnetosphere as revealed by the nonlinear analysis of in situ observations. These results constitute the solid base for the solution of the durable controversy about the chaotic or non-chaotic character of the magnetospheric dynamics. During the last two decades the concept of low dimensional chaos was supported by theoretical and experimental methods by our group in Thrace and others scientists, as an explicative paradigm of the magnetospheric dynamics including substorm processes. In parallel, the concept of self-organized criticality (SOC) and space–time intermittency was introduced as new and opposing to low dimensional chaos concepts for modeling the magnetospheric dynamics. Novel results concerning the nonlinear analysis of in situ space plasma data (magnetic–electric field, energetic particles and bulk plasma flow time series) obtained by the Geotail spacecraft presented in this paper for the first time reveal the following: (a) Coexistence of SOC and chaos states in the magnetospheric system and global phase transition from one state to the other during substorms. (b) Strong intermittent turbulent character of the magnetospheric system at the SOC or the low dimensional chaos states. (c) Clear indications for non-extensivity and q -Gaussian statistics during periods of low dimensional and chaotic dynamics of the magnetosphere. (d) Low dimensional and nonlinear space plasma dynamics in the day side magnetopause and bow shock dynamics. The dual character of the magnetospheric dynamics including low dimensional chaotic (coherent) and high dimensional turbulent states, as supported in this paper, is in agreement and verifies previous theoretical and experimental studies.