Quantifying Nocturnal Rest-State Instability Using a Thermodynamic Potential Landscape: Evidence from Population-Scale Actigraphy

Background: Traditional sleep medicine often relies on subjective questionnaires, whichprovidelimitedobjectivephysiologicalcharacterization. Whilewearableactig- raphyprovidescontinuousdata, standardmetricsfailtocapturetheunderlyingtran- sition dynamics of the sleep-wake cycle. We propose a non-equilibrium statistical physics framework to quantify nocturnal rest-state instability and its relationship with clinical confounders using hourly actigraphy. Methods: We analyzed hourly physical activity monitor data from 5,124 par- ticipants in the NHANES 2013-2014 cohort to derive physical metrics. The rest- activity sequence was modeled as a first-order discrete-time Markov model to cal- culate the nocturnal transition probability (P01) and transition entropy. Using an effective coarse-grained model, we reconstructed the empirical potential well (U (x) =−ln(P (x))) to visualize the “Rest Well” topology. A restricted cohort of 4,789 participants with complete clinical data was used for multivariate logistic regression to control for age, BMI, and PHQ-9 depression scores. Results: Our analysis revealed that subjects with sleep disorders exhibited a shal- lower nocturnal “rest well” (∆U ≈0.07), signifying a higher escape rate from the low-activity state. Global transition entropy showed a weak negative association with aging (r =−0.186, p < 0.001); in contrast, the directional transition probabil- ity P01 served as a more specific marker of sleep instability. Although the absolute shifts in these dynamical metrics were subtle, they revealed a statistically significant deviation in nocturnal rest-state stability, consistent with escape-rate theory derived from stochastic dynamics. In the full multivariate model, this physical instability was heavily mediated by depression (OR = 1.837, p < 0.001), suggesting it is a downstream physical manifestation of psychiatric burden rather than an indepen- dent etiology. Conclusion: By integrating Markovian dynamics with thermodynamic potential landscapes, we objectivelyquantifiedhow clinicaldisorderslike depressionphysically destabilize the circadian rest state. These findings support a scalable framework for digital phenotyping using wearable actigraphy, enabling objective assessment of circadian rest-state instability. This manuscript is a preprint and has not yet undergone peer review. The findings should therefore be interpreted as preliminary.