Dynamical phase transitions in Kob–Andersen model investigated by trajectory energy-biased ensemble method

Abstract

Statistical mechanics of far-from-equilibrium systems requires trajectory-based ensembles rather than static configurations. Biasing fields conjugate to dynamical activity (s-field) and time-integrated trajectory energy (g-field) provide powerful tools for probing rare dynamical states. While s-ensemble studies have demonstrated first-order dynamical phase transitions in glass-forming models, it remains unclear whether energy-only biasing can induce transitions in kinetic observables to which it is not directly coupled. Here, we investigate this question in the Kob–Andersen binary Lennard–Jones model by constructing the two-dimensional (T, g) phase diagram using transition path sampling. We identify a first-order dynamical phase transition line separating active and inactive trajectory phases, confirmed by diverging dynamical susceptibilities and bimodal order parameter distributions. Binder cumulant analysis, enabled by Gaussian process regression and large-deviation relations, locates the upper critical point (Tuc, guc) ≃ (0.675, 1.9 × 10−3). We further demonstrate that g-ensemble glasses are structurally indistinguishable from conventionally quenched glasses, while intermediate scattering functions confirm that the active–inactive transition is purely dynamical in nature. Spatial analysis further reveals that mobile particles form a system-spanning cluster in the active phase but remain fragmented in the inactive phase, consistent with the dynamical facilitation picture. These results demonstrate that energy-landscape biasing alone is sufficient to drive first-order dynamical phase transitions in an atomistic glass-forming model, establishing the g-ensemble as a controlled framework that connects the thermodynamic potential energy landscape with dynamical arrest phenomena central to kinetic theories of the glass transition.