Sure. I think even more interesting than the ratio / frequency argument is the argument that if you check whether the ice cube has coalesced, then that brings you into the system too, and now you can prove that the entropy increase from checking is, in expectation, larger than the entropy decrease from the unlikely chance that you find an ice cube. Repeat many times and the law of large numbers guarantees that this procedure increases entropy. Hence no perpetual motion. Well anyway, that’s the part I like, but I’m not disagreeing with you. :-)
Sure. I think even more interesting than the ratio / frequency argument is the argument that if you check whether the ice cube has coalesced, then that brings you into the system too, and now you can prove that the entropy increase from checking is, in expectation, larger than the entropy decrease from the unlikely chance that you find an ice cube. Repeat many times and the law of large numbers guarantees that this procedure increases entropy. Hence no perpetual motion. Well anyway, that’s the part I like, but I’m not disagreeing with you. :-)