A Landau-Ginzburg Phenomenology of Sleep-Stage Transitions

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Original abstract

Sleep staging provides a reproducible clinical description, but it does not by itself explain why some boundaries are abrupt while others are graded, or why transition windows contain instability, synchrony, and apparent state coexistence. We develop a local Landau-Ginzburg phenomenology in which each boundary is represented by motion in an effective potential of a spatially extended, noisy, dissipative neural field. A latent cortical-ordering coordinate phi is inferred from prespecified EEG/PSG observables through a measurement model designed to avoid circularity. The canonical boundaries are treated separately. Existing data support a fold-like loss of wake stability at sleep onset; whether that fold lies on a globally bistable cusp with hysteresis remains open. N1-to-N2 and N2-to-N3 are posed as continuous-like ordering crossovers, NREM-to-REM as a candidate first-order-like desynchronizing switch, and a possible within-N3 mixed or tricritical-like regime as a speculative hypothesis. The Ginzburg term adds spatial predictions - growth of correlation length and local-to-global recruitment - that are absent from scalar sleep-onset models. We specify the evidence needed to distinguish bifurcation, coexistence, noise-driven escape, smooth crossover, and scoring-induced discontinuity. Illustrative time-dependent Ginzburg-Landau simulations reproduce the proposed signature classes. A synthetic classification experiment partially distinguished six archetypes (cross-validated accuracy 0.49 +/- 0.005; balanced baseline 0.17), with little change under a noise-regime shift. These analyses establish the internal consistency and testability of the framework, not the proposed taxonomy in human sleep. Transition-centered EEG validation is required before clinical or neuromodulation applications are pursued.

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