Stationarity measure of solar wind in the outer heliosphere

The thermodynamic behavior of the solar wind (SW), particularly under non-Maxwellian conditions, is often described by kappa distributions. However, the role of pickup ions (PUIs) and their impact on thermodynamic stationarity in the outer heliosphere remains insufficiently quantified. This study investigates the thermodynamic stationarity of kappa- distributed SW protons, including the contribution of PUIs, and examines their radial evolution across the heliosphere. We employed the stationarity measure, defined as the ratio of the Boltzmann–Gibbs entropy deviation to the thermodynamic kappa parameter, along with its scaling exponent with kappa deviation: the stationarity deviation index (SDI). Using plasma observations from Ulysses/SWOOPS (1.8–3.2 au) and New Horizons/SWAP (∼20.5–60 au), we derived the radial profiles of the SDI. We find that (i) both the entropy deviation ratio and the SDI increase when kappa-distributed SW protons are analyzed together with nonstationary pickup protons; (ii) the SDI exhibits a pronounced radial dependence, increasing from ∼1 to ∼42 au, peaking near 42 au, followed by a sharp decrease to ∼51 au and a more gradual decline out to ∼60 au; and (iii) across shocks, the overall stationarity of the total proton population remains approximately constant, while the SDI systematically increases from upstream to downstream regions. The inclusion of PUIs significantly modifies the inferred thermodynamic stationarity of SW protons. The observed radial trends and shock-related variations in the SDI have important implications for our understanding of the thermodynamic evolution of heliospheric plasmas and in modeling studies of non-equilibrium processes in the outer heliosphere.