From what I have understand, heat death of the universe requires a positive cosmological constant. And so when the universe achieves thermodynamic equilibrium, it shall have maximum entropy.

Now I have several confusions arising out of this, mostly because I think I am missing certain points.

  1. Doesn't it feel like then the universe shall have uniform probability distribution of indivisible particles which yields randomness? Then, do random systems have large amount of information associated in the form of high entropy?

  2. Moreover, how do you quantify entropy due to gravity?

  3. Also, given the no-hiding theorem (which states the conservation of quantum information) how should entropy of the universe be increasing? Does it mean that we are not in a closed information system?

If you know any good resources to understand the above, please mention here too.