Uncertainty-aware Bayesian inference of glass transition temperatures from molecular simulations

The glass transition temperature, Tg, is a central thermophysical parameter in polymer physics, yet its extraction from molecular simulation data is typically performed using deterministic piecewise fits that assume abrupt separation and provide no rigorous quantification of uncertainty. In this work, we reformulate glass transition estimation as a Bayesian inference problem, in which Tg is treated as a latent thermodynamic parameter, and the transition is modeled explicitly as a finite-width crossover in the temperature-dependent specific volume. This probabilistic formulation yields full posterior distributions for both the transition temperature and its breadth, enabling uncertainty arising from finite sampling, temporal correlations, and discrete temperature grids to be propagated consistently. Applying the framework to coarse-grained polymer melts spanning chain lengths from N = 25 to N = 500, we show that the smooth crossover description is consistently favored over a conventional change-point formulation according to information-theoretic model evidence. The inferred posterior median Tg increases systematically with molecular weight, while both the uncertainty in Tg and the transition width decrease, reflecting the progressive sharpening of the thermodynamic crossover as finite-size and chain-end effects diminish. Posterior predictive analyses further demonstrate that a single model structure and likelihood specification remain statistically calibrated across all chain lengths without system-specific adjustment. By unifying thermodynamic modeling, uncertainty quantification, and model evidence within a single framework, this work establishes an uncertainty-aware and transferable methodology for extracting glass transition temperatures from molecular simulations and replaces heuristic fitting procedures with statistically grounded thermodynamic characterization.