One [obvious] way to remove a seized nut is to heat it [thus enlarge it]... more than the bolt. But that's not the only way to use heat in this application. Apparently you can also let the stuff cool down and the nut will still be significantly easier to remove than before applying theat. Why does this happen? The description of this latter video says something about heat "separating the corrosive bonds". Is there real science behind this claim?
If by corrosive bond they mean a physical bond not a chemical bond then yes, there is a very strong force of dry friction between the two parts.
Bolts and nuts are made so that the two fit together tightly so that they do not wiggle loose but not so tight that they are impossible to fasten. The problem is is that when iron corrodes the oxide has more volume than the iron. In fact when iron oxidizes, its size increases 70% (See: Pillings-Bedworth ration). This expansion puts a lot of force between the nut and the bolt. Since dry friction increases linearly with force, friction between the two increases also making the bolt harder to remove.
When you expand the nut and/or shrink the bolt some of this force is relieved and friction decreases making the nut easier to turn.