There appears to be a correspondance between thermal entropy and gravitational entropy with one converting into the other interchangeably, just like kinetic energy can be converted into potential energy and and then back again, indefinitely in an ideal oscillating system. Is it possible that there is an interplay between gravitational entropy and thermal entropy (and the various other forms of entropy such as entropy of mixing and information entropy etc) that conserves total entropy? How well do we understand all the various forms of entropy and how they interelate?
Take a cloud of gas molecules in open space. They expand and we say that is example of increasing entropy because the molecules are dispersing. Then take a cloud of gas molecules on a larger scale and they gravitationally collapse and we also say that is example of increasing entropy. So whether molecules disperse or clump together we say it is increasing entropy. Of coure the difference is due to scale and gravity but that is the important point. Entropy is not just about thermal entropy. Now let's take the extreme example of a large cloud of gas molecules clumping to form a black hole. Hawking provides us with an equation for the entropy of a black hole and shows it has greater entropy than the dispersed cloud of molecules. Fine, but hang around a while and the black hole evaporates to become a ...wait for it... a dispersed cloud of molecules. Now that seems to contradict my previous statement. Whether a cloud of molecules clumps to form a black hole or black hole evaporates to become a cloud of molecules, we say both are examples of increasing entropy. Of course, black holes only evaporate when the universe has expanded and cooled suffiently for the the black hole to lose more due to radiation than it gains from absorbing the background CMB. The important thing to notice is the interplay between the size of the universe, gravity and entropy. Imagine a very late stage universe where all the black holes have evaporated to form a very dispersed cloud of radiation and molecules and then starts collapsing. (If I recall correctly the gravitation of a radiation dominated universe is greater than that of a matter dominated universe). So if the universe is one dispersed cloud of atoms and radiation and it collapses to form one big black hole then the collapse of the universe is an example of increasing entropy because that is what Hawking's equation says.
