Configurational entropy and diffusivity of supercooled water

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Abstract
As a liquid approaches the glass transition, its properties are dominated by local potential minima1,2 in its energy landscape. The liquid experiences localized vibrations in the basins of attraction surrounding the minima, and rearranges via relatively infrequent inter-basin jumps3. As a result, the liquid dynamics at low temperature are related to the system's exploration of its own configuration space. The ‘thermodynamic approach’ to the glass transition considers the reduction in configuration space4,5,6,7,8 explored as the system cools, and predicts that the configurational entropy5,9,10 (a measure of the number of local potential energy minima sampled by the liquid) is related to the diffusion constant. Here we report a stringent test of the thermodynamic approach for liquid water (a convenient system to study because of an anomalous pressure dependence in the diffusion constant). We calculate the configurational entropy at points spanning a large region of the temperature–density plane, using a model11 that reproduces the dynamical anomalies of liquid water. We find that the thermodynamic approach can be used to understand the characteristic dynamic anomalies, and that the diffusive dynamics are governed by the configurational entropy. Our results indicate that the thermodynamic approach might be extended to predict the dynamical behaviour of supercooled liquids in general.