You posted: "There is nothing in the 2nd law about densities, is there?"
The differing densities and the gravitational field provide tabular order; you could apply the 2nd law to a set of encyclopaedias with equal relevance.
Next try the experiment with two beakers; one with miscible liquids, and the other with immiscible liquids. Describe your results. Keep trying to find a connection to the thermodynamics of an infinite system, while turning blue in the face."
Reply:
Cute. You know about miscible liquids--puts you a step above most creationists. I don't know why you specified beakers--this was kitchen-observable science. You don't need beakers or a lab to observe order arising spontaneously out of disorder. Any middle school student can do this experiment and see the results.
Now: I did not claim this works with any two different liquids. I said oil and water. It works with mercury and benzene, too, in case you are confused. You go on to talk about "the thermodynamics of an infinite system". I have no idea what this means. I only post what we observe here on planet earth.
And: Please show us where miscible/immiscible liquids are mentioned in the 2nd law.
Your stubborn ignorance transcends my patience (yes, I know, patience is a virtue, but do pigs wear pearls?)
One of the problems with discussions such as the present one is that the parties do not take the trouble to provide a clear and unambiguous statement of what they mean by the "Second Law."