Structural vs dynamical estimators of the excess entropy of water across its phase diagram

The excess entropy is a fundamental thermodynamic observable for understanding the properties and anomalous behavior of liquid water. Barring computationally intensive methods such as thermodynamic integration, rapid and accurate routes to the excess entropy remain somewhat elusive. Previous attempts have relied on the two-body translational entropy alone or, more rarely, on additional calculations of the two-body orientational entropy, both of which are structure-based entropy estimators. In this work, we demonstrate that the Two-Phase Thermodynamics (2PT) method, a dynamical entropy estimator based on the velocity density of states (VDOS) function, provides a robust, efficient route to estimating the excess entropy of liquid water across a wide range of state points (220 ≤ T ≤ 360 K, 0.85 ≤ ρ ≤ 1.3 g/cm3). The VDOS reflects the collective dynamics of all atoms in the system, such that 2PT implicitly recovers information equivalent to the higher-order correlations neglected by S2, without requiring their explicit evaluation. Thus, we show that the 2PT excess entropy follows the experimental reference closely through all the state points considered, using four different empirical water models. Comparison against more rigorous transition-matrix Monte Carlo simulations, which share the force field and thus separate model error from method error, apportions the residual offset from experiment as roughly two-thirds inherent deficiencies in the force field and one-third the 2PT analysis itself.