I would argue it depends on the nature of the system. If the system follows (simple) rules then you can likely compress the description of the system into somet

I would argue it depends on the nature of the system. If the system follows (simple) rules then you can likely compress the description of the system into something that fits into a (small) subsystem. If the system and its behavior is a uncompressible mess this will not work out. Up to now, I would say, our universe with all its relatively simple laws of physics looks pretty structured and easily compressible.