Non-extensive (Tsallis) q-statistics and auroral glow

Physica A: Statistical Mechanics and its Applications. 2024. Vol. 639. Article 129661.

Chernyshov A., Kozelov B. V., Mogilevsky M. M.

It is well-known that the auroral region of the magnetosphere–ionosphere interaction is an open, nonlinear dissipative system far from the equilibrium state. It is in this region that auroras are regularly observed, demonstrating not only a wide variety of dynamic forms but also a wide range of temporal and spatial scales. Due to the memory effects and fractal properties of auroral plasma, as well as strong correlations between its individual parts, the dynamics of the
high-latitude system are primarily determined by long-range electromagnetic forces. Therefore, it is expected that non-additive and non-extensive thermodynamic principles may characterize their macroscopic behavior. In the presented study, it is shown that pulsating auroras exhibit non-extensive properties and can be described by q-statistics. The correlation of the parameter 𝑞 with traditional indicators of nonlinear dynamics, such as the flatness coefficient, standard deviation, and scaling index, has been investigated. Small-scale changes are superimposed on large-scale processes characterized by a low correlation dimension, and this leads to an increase in the correlation dimension during geomagnetic activity, which approximately coincides with increased values of 𝑞. It is concluded that the q-statistics (Tsallis distribution) can be used to analyze optical phenomena in the auroral region.

Keywords: correlation dimension, корреляционная размерность, неэкстенсивная термодинамика, Non-extensive q-statistics, auroras, auroral ionosphere, полярные сияния, авроральная ионосфера