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Epigenetic clocks based on DNA methylation patterns are among the most accurate molecular correlates of chronological age, yet widely used clocks are predominantly empirical models with limited explicit characterization of the underlying methylation variability, lacking a direct connection to the physical mechanisms of aging. In this work, we bridge this gap by introducing an information-theoretic framework for DNA methylation dynamics combined with nonlinear machine learning to develop a competitive and interpretable age predictor. We model the population distribution of methylation β -values at each CpG site using a reparameterized three-parameter Generalized Gamma Distribution (GGD) and derive a closed-form expression for its differential Shannon entropy. The resulting CpG-level entropy is used to characterize methylation variability and as a criterion for locus filtering. We introduce the Stacy Gradient Boosting Clock (Stacy-GB), which combines this GGD-based representation with a LightGBM regressor. The model was evaluated across independent cohorts using the ComputAgeBench epigenetic clock benchmark. Stacy-GB achieved a mean absolute error (MAE) of 3.74 years and a median error (bias) of 2.41 years, significantly outperforming state-of-the-art epigenetic clock baselines. Furthermore, age acceleration estimated by Stacy-GB was associated with several clinical pathologies, including ischemic heart disease, HIV infection, multiple sclerosis, and Werner syndrome, supporting its potential as an accurate and biophysically grounded tool for clinical aging research.