I don't think it's arbitrary. You even distinguished in this comment between a brain and a simulation of a brain. Steel is a physical system that can be modeled mathematically. Accurately simulating steel doesn't make steel.
Agreed. I think radioactive decay is an even better example of a well modeled physical system that defies simulation. A simulation of an ounce of decaying uranium won't tell you which atoms will decay in which order in a physical chunk. Ergo, somethings defy simulation.