EEG Microstate Aggregate Conditional Entropy Derived from Markov Modelling as a AD-Specific Biomarker: Differentiating Alzheimer’s Disease from Frontotemporal Dementia and Healthy Controls

Background: The resting brain sustains spontaneous spatiotemporal fluctuations that theoretical and empirical accounts propose are organised near a critical phase transition, a regime associated with maximal information processing capacity. Departures from this regime-manifesting as constrained transition structure in the neural dynamics-have been implicated in neurological and neurodegenerative disorders that includes Alzheimer’s disease (AD). Existing metrics for quantifying transition-structure diversity overwhelmingly depend on functional MRI, limiting clinical accessibility. EEG microstates-quasi-stable scalp potential topographies persisting 60-120 ms-provide a high-temporal-resolution, low-cost window into large-scale brain dynamics. No prior work has applied information-theoretic Markov modelling to the microstate transition sequences in order to derive a physics-grounded, information-theoretic transition-diversity metric for differentiating AD from healthy controls. Methods: Resting-state EEG from 85 participants (healthy controls [HC]: n = 27; AD: n = 35; frontotemporal dementia [FTD]: n = 23) was retrieved from the publicly available OpenNeuro dataset ds004504. Preprocessing consisted of bandpass filtering (1-40 Hz), average re-referencing, and independent component analysis (ICA) artefact rejection implemented in MNE-Python. EEG microstates were extracted via modified K-means clustering (K = 4) applied to global field power (GFP) peak topographies. A Markov transition model was inferred per participant and the aggregate conditional entropy ACE(T) was computed as a scalar transition-diversity biomarker. Group differences were assessed by Kruskal-Wallis and using post-hoc permutation tests (N = 10,000; α = 0.05); the diagnostic classification was evaluated by ROC analysis. Performance was compared against the theta/alpha spectral power ratio as the primary benchmark. A parameter-matched comparison with permutation entropy (PeEn) and sample entropy (SampEn) was not feasible under the speed-optimised conditions applied here therefore these measures require recomputation under the standard conditions before a meaningful benchmark comparison can be drawn. Results: A significant group difference in the ACE(T) was observed (Kruskal-Wallis: H(2) = 7.464, p = 0.024; η² = 0.067 ). AD participants exhibited significantly reduced ACE(T) relative to HC (ΔACE = 0.067 bits; Cohen’s d = 0.705; permutation p = 0.007, Holm-corrected p = 0.021), yielding an AD vs. HC classification AUC of 0.691 (95% CI: 0.555-0.819), consistent with more constrained microstate transition structure. AD was significantly different from FTD (ΔACE = −0.066 bits, d = −0.642, Holm-corrected p = 0.042). FTD participants did not differ significantly from HC (permutation p = 0.963; AUC = 0.517), a null result that reflects insufficient statistical power (n = 23; minimum detectable d = 0.811) rather than confirmed disease specificity. The theta/alpha ratio outperformed ACE(T) (AUC = 0.765); ACE(T) offers complementary interpretability and theoretical grounding. Significance: Markov-model-derived aggregate conditional entropy of EEG microstate sequences yields an interpretable, theory-grounded transition-diversity biomarker capable of differentiating AD from HC without any recourse to deep learning or MRI infrastructure, offering potential utility for scalable neurological screening in low-resource settings.