Yes I left out the part about steady state condition as well as absolute zero temperature condition, because those are boundary conditions (constant conditions)

Yes I left out the part about steady state condition as well as absolute zero temperature condition, because those are boundary conditions (constant conditions) that don't involve time. My point is about an integral over all time. And yes the definition of "universe" is something I define as "a closed system that doesn't interact with other systems", which is also a consistent definition even if the multiverse theory is correct. If two things interact then they are by definition in the same universe.