Why can’t the daemon just continuously look at a tiny area around the gate and decide just based on that? A tiny area seems intuitively sufficient for both recognizing that a molecule would go from left to right when opened, and no molecule would go from right to left. This would mean that it doesn’t need to know a distribution over molecules at all.
Basically: Why can’t the daemon just solve a localised control task.
Why can’t the daemon just continuously look at a tiny area around the gate and decide just based on that? A tiny area seems intuitively sufficient for both recognizing that a molecule would go from left to right when opened, and no molecule would go from right to left. This would mean that it doesn’t need to know a distribution over molecules at all.
Basically: Why can’t the daemon just solve a localised control task.
The daemon can indeed do that, and the theorem in the post is compatible with such a daemon.