Just when I thought I was getting an intuition about entropy...
I read in a Q&A here that the only way to lower the entropy of a system is to cool it. I gave that more thought, and I understand it to be true since a hotter substance will have molecules more spread out and randomly dispersed => more possible arrangements of the molecules present => more disorder => higher entropy. So, unusual exceptions aside, higher temperature = higher entropy.
Then I consider the theory that the universe is cooling and its entropy increasing, potentially leading to the 'heat death' of the universe when we reach maximum entropy and absolute zero temperature. Am I misunderstanding this theory?
How can it be true that higher temperature = higher entropy of a system, and yet maximum entropy for the universe would be the maximum dispersal of heat and thus ultimately-low temperature? Is it that for open systems, higher temperature = higher entropy, but for closed systems, gradual cooling and gradual creation of entropy goes together?