Second, third and correlation moments from nonequilibrium and equilibrium fluctuation theory, N, P, T ensemble, compared between supercooled and superheated liquid water

A local nonequilibrium fluctuation (NEF) theory has been developed which applies to modest deviations from equilibrium when gradients, time dependences, etc., are absent, and, provided that long-range spatial correlations of the fluctuations are suppressed, for example, by droplet sizes down to 3 μm required to obtain thermodynamic data at the extremes of supercooling. The predictions from NEF theory are constrasted against those from equilibrium fluctuation (EF) theory using the extensive data available for metastable liquid water. NEF and EF second and third T and P moments were calculated and compared between the maximum supercooling and superheating spinodals, ≈227 K and ≈596 K, at 1 atm pressure. The EF second and third T and P moments are either small or zero near 227 K, but 〈(δT)2〉 and 〈(δP)2〉 approach +∞ near 227 K, and 〈(δT)3〉 and 〈(δP)3〉 approach -∞ and +∞, respectively, when calculated by NEF theory. Moreover, all NEF second moments, G, A, H, E, P, V, T and S, approach +∞ for supercooled water near 227 K, and correlation moments, e.g., entropy-pressure, also diverge. The positive infinities in 〈(δP)3〉 and 〈(δP)3〉 require some pressure fluctuations to reach the negative-pressure stability limit of supercooled water at 227 K, thus causing mechanical instability, but mechanical instability at 227 K is not obtained from EF theory. An even more important result is that the NEF second S moment diverges much faster near 227 K then the EF second S moment. This occurs because the NEF second S moment contains two diverging terms; the first is the same as the EF second S moment, but the second, more-rapidly diverging term, is related to the nonequilibrium entropy production. The NEF second E moment also is somewhat larger than the EF second E moment near 227 K, whereas other second moments, of A, H and V, are identical in EF and NEF theory. Several NEF second moment divergences do not result just from the infinities in the individual susceptibilities, but rather from the product of CP, β, or KT, with 1/(CVKT+βV), which also approaches large values near 227 K. Differences between NEF and EF results also occur up to 596 K for superheated water.