This is the answer. Some truly random events, the molecular and atomic movements that we perceive as heat, just don't matter. So many gas molecules exist, and they move so often, individual, random movements don't matter.

There's also that weird fractal scale issue. Take the edge of a pond. From a distance, 30 feet or so, the edge of the water is distinct. But the closer you get, the less distinct it gets. Some plants are growing in the water. Some pond water is in the first few inches of bank. Dig a little down and you find "pond" even farther out into the banks.

Sure, technically, the first random event might be different, but it almost certainly won't matter. There will be a mysterious period of staying in synch.