Tracking nonlinear solar-wind dynamics over three solar cycles using Wind observations

The solar wind is a turbulent, weakly collisional plasma characterized by non-Gaussian fluctuations, long-range correlations, and multifractal dynamics. We investigate the long-term evolution of these properties using hourly proton density measurements obtained directly by the Wind spacecraft over 1995--2025. The use of a single-spacecraft dataset provides an independent test of previous results derived from the multi-spacecraft OMNI database. The three components of the nonextensive q-triplet are estimated within one-year sliding windows shifted monthly: qₛₜₐₜ from the distribution of density increments, qᵣₑₗ from the decay of the autocorrelation function, and qₛₑₙₛ from the multifractal spectrum. Their mean values, qₛₜₐₜ=1.71±0.07, qᵣₑₗ=4.62±0.52, and qₛₑₙₛ=-0.45±0.27, confirm the persistent presence of heavy-tailed statistics, slow relaxation, and weakly chaotic multifractal dynamics. The parameters nevertheless exhibit distinct temporal variability and relationships with solar activity. The Fourier spectrum of qₛₜₐₜ contains a dominant period of approximately $10.1$ years, while its correlation with the sunspot number is positive and moderate ($r=0.611$). Correlation and mutual-information analyses show that qₛₜₐₜ is primarily associated with solar proxies, whereas qₛₑₙₛ displays stronger relationships with geomagnetic indices and qᵣₑₗ exhibits weaker dependencies. An anomalous enhancement of the q-triplet around 2004 is possibly related to Wind's orbital transition. These findings support the robustness of the nonextensive description and show that the statistical and dynamical properties of solar wind proton density show evidence of modulation by solar activity.