If you don’t have an observer in the system, you instead have an observer outside the system, and in order to actually be observing must be interacting with the system—in which case the system is no longer closed, and therefore, simplistic statistical mechanics is no longer sufficient, and you have to bring in all the open-system math.
If you don’t have an observer in the system, you instead have an observer outside the system, and in order to actually be observing must be interacting with the system—in which case the system is no longer closed, and therefore, simplistic statistical mechanics is no longer sufficient, and you have to bring in all the open-system math.