Is water one liquid or two?

The idea that water is a mixture of two distinct states is analyzed in some detail. It is shown that the known compressibility of water is in fact sufficiently small that for a volume of water of size 1 nm³, the density fluctuations are of order 4% of the average density. This is much smaller than the ≈25% density fluctuations that would be required for significant regions of high and low density water to occur on this volume scale. It is also pointed out that the density fluctuations in water are, if anything, smaller than those that occur in other common liquids which do not have the anomalous properties of water. It is shown that if the distribution of density fluctuations is unimodal, the system is in the one-phase region, and if bimodal, it is in the two-phase region. None of the liquid or amorphous phases of water explored in this work give any sign of being in the two-phase region. Existing neutron and X-ray scattering data on water in the amorphous phases, and in the stable liquid phases as a function pressure and temperature, are subject to a new set of empirical potential structure refinement simulations. These simulations are interrogated for their configurational entropy, using a spherical harmonic reconstruction of the full orientational pair correlation function. It is shown that the excess pair entropy derived from this function, plus the known perfect gas contributions, give a reasonable account of the total entropy of water, within the likely errors. This estimated entropy follows the expected declining trend with decreasing temperature. Evidence that higher density water will have higher entropy than lower density water emerges, in accordance with what is expected from the negative thermal expansion coefficient of water at low temperatures. However, this entropy increase is not large and goes through a maximum before declining at yet higher densities and pressures, in a manner reminiscent of what has been previously observed in the diffusion coefficient as a function of pressure. There is no evidence that ambient water can be regarded as patches of high density, high entropy and low density, low entropy liquid, as some have claimed, since high density water has a similar entropy to low density water. There is some evidence that the distinction between these two states will become more pronounced as the temperature is lowered. Extensive discussion of the use of order parameters to describe water structure is given, and it is pointed out that these indices generally cannot be used to infer two-state behavior.