[Kednicma]

You're not wrong, but the connection's already explored well; we call it "chemistry". Cook a piece of chalk and it'll crumble into powdery lime; mix it with water and air and it'll heat up and set back into hard stone.

The bigger idea here is that, while it's highly improbable that heat is applied to chalk, we can choose to apply heat to chalk. We have the choice of where to direct our energy. This is, by the Free Will Theorem, the same choice that subatomic particles make about how their energy will be measured. The loophole is precisely that if enough particles choose to synchronize their choices, then they can make highly structured choices with rich data for a long period of time; they can integrate information.

When we crumble the chalk, we lose the specific information about the shape of the chalk, and it would be very hard to recreate; this is entropy. But we also gain the specific information about the shape of the cement, and this would be very hard to determine from the prior context of the universe; this is choice and integrated information.

[im3w1l]

I think this is not what I meant. Let me restate your point as I understand it with a more well known example.

Melt a piece of ice and it will turn into water. Cool it and it will turn back into ice. The bigger idea here is that, while it's highly improbable that heat is applied to ice, we can choose to apply heat to ice. (...)

When you are heating the ice, energy and entropy from the environment is stored in the ice. When you are freezing it, energy and entropy from the water is transferred away to the environment.

This is a different thing from what I was talking about.