We know that at the end computation should be done by physical systems which follow laws of physics. I know there are some researches that study the phase transition phenomenon in physics and try to connect it with some properties in complexity theory (such as P and NP famous problem ). Just a quick review for example the phase transition happens from 2-SAT problem to 3-SAT problem. The first one is in P and the second one is NP-Complete.
My question is that: Is there any study that shows the mapping of Polynomial Hierarchy (PH) and multi-phase systems? Is there any mapping between PH-Complete problems and real physical system states? If so, are all levels of these hierarchy stable?