Treffer: Temporal Differentiation of Sleep Stages via the Negentropic Stabilization Index

Temporal Differentiation of Sleep Stages via the Negentropic Stabilization Index (NSI) – Version 2.0 This preprint presents an updated and extended version of our initial study on the Negentropic Stabilization Index (NSI), a novel entropy-based measure designed to capture temporal organization in EEG signals. The NSI quantifies the directional stability of entropy over time and is proposed as a potential biomarker for transitions between distinct states of consciousness during sleep. Key contributions of version 2.0 include: Expanded dataset: Analysis across three subjects using Sleep-EDF data with two EEG channels (Fpz–Cz and Pz–Oz). Temporal segmentation: Stream-based NSI computation to overcome memory constraints on long recordings. Statistical analysis: Kruskal–Wallis and Dunn post-hoc tests show significant differentiation between sleep stages, especially between wakefulness and NREM2. Methodological transparency: All data, preprocessing pipelines, and source code (in Jupyter notebook format) are included for full replication. Theoretical framing: The study discusses NSI in the context of neurophysiological order, entropy gradients, and the temporal structure of consciousness. Roadmap: This study is the foundation for future research incorporating reinforcement learning validation and broader EEG datasets. Limitations: The current version is based on a small pilot sample (N=3) and Sleep-EDF recordings only. Further validation is required across larger and more diverse populations and against alternative entropy measures. This dataset and code archive accompany the manuscript and provide a replicable foundation for researchers interested in the intersection of entropy dynamics, sleep neurophysiology, and the emergence of temporal structure in biological systems.
This preprint presents a pilot study exploring the Negentropic Stabilization Index (NSI) as a novel metric for quantifying temporal dynamics of EEG during human sleep. NSI is based on the temporal derivative of entropy and is proposed as a candidate marker of the emergent structure of time and possibly even consciousness. The analysis was conducted on EEG recordings from the Sleep-EDF Expanded database, focusing on two canonical channels (Fpz–Cz and Pz–Oz) across five classical sleep stages (W, N1, N2, N3, REM). NSI values were computed using sliding entropy windows and statistically compared across sleep phases. The results show that NSI significantly differentiates sleep stages, especially between wakefulness (W) and light sleep (N2), confirming its potential to reflect phase transitions in neural dynamics. The study includes: Theoretical background of NSI, Methods for EEG preprocessing and NSI computation, Statistical results (Kruskal–Wallis and Dunn post-hoc tests), Open-source datasets (clean EEG+NSI tables), A reproducible Python notebook for validation. This research builds on the theoretical framework introduced in: Hrubec, K. (2024). The Relational Nature of Time and its Role in Consciousness. Academia.edu. https://www.academia.edu/126670497 Hrubec, K. (2024). Altered States of Consciousness and the Perception of Time: An Entropic Perspective. Academia.edu. https://www.academia.edu/127499112