Water memory was a controversial experiment claiming to provide an explanation supporting homeopathy. The results were largely dismissed as being tainted by experimental error.
One possible mechanism invoked was that water molecules, on account of being polar, would form a structured network, thus storing information about other molecules they had been in contact with. I wonder if it is possible to disprove this explanation with an entropy argument. If water molecules did arrange themselves in such a fashion, this would have an effect on their entropy, which in turn would impact other thermodynamic functions such as Gibbs free energy. In other words, it might be possible to look for such an entropic effect by looking at deviations from expected behavior in a steam table. Would the magnitude of such an effect be measurable ?