What Defines Stationarity in Space Plasmas

Starting from the concept of entropy defect in thermodynamics, we construct the entropy formulation of space plasmas, and then use it to develop a measure of their stationarity. In particular, we show that the statistics of this entropy results in two findings that improve our understanding of stationary and nonstationary systems: (i) variations of Boltzmann−Gibbs (BG) entropy do not exceed twice the value of the thermodynamic kappa, the parameter that provides a measure of the entropy defect in both stationary and nonstationary states, while becoming the shape parameter that labels the kappa distributions in stationary states; and (ii) the ratio of the deviation of the BG entropy with kappa scales with the kappa deviation via a power law, while the respective exponent provides the stationarity deviation index (SDI), which measures the natural tendency of the system to depart from stationarity. We confirm the validity of these findings in three different heliospheric plasma data sets observed from three missions: (1) a solar energetic particle event, recorded by the Integrated Science Investigation of the Sun instrument on board the Parker Solar Probe; (2) near-Earth solar wind protons recorded by the Solar Wind Experiment instrument on board Wind; and (3) plasma protons in the heliosheath, the source of energetic neutral atoms recorded by Interstellar Boundary Explorer. The full strength and capability of the entropic deviation ratio and SDI can now be used by the space physics community for analyzing and characterizing the stationarity of space plasmas, as well as other researchers for analyzing any other correlated systems.