Global complexity signatures of solar cycles: a unified entropy–fractal survey of OMNI solar wind data (1964–2025)

Abstract

Background — Traditional solar-cycle studies emphasize amplitude- and duration-based indicators, overlooking the intrinsic complexity of heliospheric fluctuations. Entropy- and fractal-based descriptors offer complementary insight, but a cycle-resolved assessment across multiple observables has been missing. Methods—Using daily OMNI-2 data (1964–2025), we segment each solar cycle (20–25) into ascending and descending phases and compute eleven global complexity measures per cycle–phase segment for ten solar-wind and geomagnetic observables. The metrics cover information content (Shannon, spectral), dynamical regularity (approximate, sample, permutation), geometric roughness (Higuchi, Katz, Petrosian), algorithmic novelty (Lempel–Ziv), and long-range memory (Hurst). We analyse redundancy and physical linkages via correlations and principal-component analysis (PCA), and quantify within-cycle phase contrasts using paired nonparametric tests with bootstrap effect sizes. Cycle parity is tested with permutation-based linear models controlling for the physical variable. Results — Two orthogonal axes summarize the landscape: an amplitude–breadth direction (dominated by Shannon/spectral entropy) and a temporal-irregularity direction (ordinal entropies and Higuchi), while Lempel–Ziv forms an almost independent third dimension. Crucially, phase—not odd/even parity—organizes the dominant variability: ascending halves maximize multiscale roughness, whereas descending halves show broader amplitude dispersion and higher algorithmic novelty. Cross-metric–observable maps tie these facets to known regimes: fast streams and composition-rich intervals (e.g., larger ω/p) raise ordinal richness and LZ; storm-time geomagnetic response (Dst, Kp) aligns with antipersistence and space-filling trajectories.