I do have a degree in Physics, so perhaps that's the source of this belief I've held - probably from countless impromptu discussions with fellow physics geeks. You wanna know the entropy of this system? Calculate it, don't eyeball it.
If 'gravity' weirds you out, put the mixture in a centrifugal chamber and let it spin. You get the same gradiated separation.
> Usually entropy makes things spread out, but gravity makes things come together. Weird.
It's no weirder than saying that hydrogen atoms exist because the proton attracts the electron.
But the attractive forces of protons and electrons ARE weird. Do know how attraction/integration can lower entropy?
This oil/vinegar example is immediately useful for other areas too. We have oil and vinegar in the dressing. They eventually become separated and we need to put effort to mix them together. Now replace oil and vinegar with leave/remain, blue/red or whatever else...
The example of oil and water is great. While they are separated with a gradient, there is no latent tendency to flow together and mix.
But, it's only gravity that makes the oil and water issue hard to understand. With no gravity, they would not be evenly divided.
We still don't understand gravity, as it relates to entropy. Usually entropy makes things spread out, but gravity makes things come together. Weird.