Sleep-stage dynamics beyond the power spectrum: A surrogate-referenced multiscale ordinal analysis

Sleep stages are commonly characterized by their EEG spectra, but spectral analysis cannot reveal whether brief voltage fluctuations follow a preferred temporal order. This study investigates whether such temporal organization varies across sleep stages and persists after controlling for amplitude distributions and power spectra. Using an open multi-night dataset, ordinal patterns were used to characterize short EEG segments according to the ordering of their values. Entropy, statistical complexity, and Fisher information provided complementary measures of this organization. Each window was compared with IAAFT surrogates preserving its amplitude distribution and Fourier magnitude, with inference performed at the participant level. Residual temporal organization was consistently observed across stages and temporal scales, with the strongest combined signature in N2 at intermediate subsecond scales. Complexity and Fisher information further distinguished N3 from N2 when entropy alone did not. Synthetic benchmarks suggested that a slowly amplitude-modulated linear oscillator better reproduced the empirical profile than a canonical chaotic system. Thus, sleep EEG exhibits stage-dependent temporal organization beyond conventional amplitude and spectral structure, without implying a unique mechanism or deterministic chaos.