Causality in liquid water as a hallmark of emergent glassy dynamics

In molecular liquids such as water, time-delayed influences between microscopic or mesoscopic variables are typically probed using time-correlation functions, which are symmetric under detailed balance and therefore blind to dynamical asymmetries. Here, we characterize water's dynamics using a causal inference metric that captures asymmetric couplings between collective variables. Analyzing equilibrium molecular dynamics simulations at ambient conditions and in the high-density liquid (HDL) regime of supercooled water, we uncover pronounced asymmetries in the couplings between orientational and translational degrees of freedom across multiple time and length scales. At room temperature, rotational modes exert a modest directional influence on translational dynamics. In contrast, in the supercooled HDL regime, translational motions emerge as the primary drivers of the dynamics, suggesting facilitation-like relaxation mechanisms characteristic of glassy systems. These results reveal a qualitative reorganization of dynamical couplings across thermodynamic conditions, implying that molecular liquids at thermal equilibrium can exhibit an emergent directionality in their fluctuation couplings. As a consequence, our analysis reveals that external perturbations acting on specific degrees of freedom can induce a stronger arrow of time in the causal relations between translational and orientational modes.