How does compounding work in Mistborn?
Brandon Sanderson (paraphrased)
I can explain this better in person because I know things that the characters in the book don’t. So, they haven’t worked a lot of this out. All the magic systems in my work are linked because the books all take place in the same universe. In Elantris, magic works by drawing symbols in the air. What actually happens is that when they draw a symbol, energy passes through it from another place (which is my get-out for the laws of thermodynamics) and the effect of that energy is moderated by the symbol. In one case it may become light, in another it may become fire. In Mistborn, the metals have a similar effect. The magic is not coming from the metal (even if some characters think it is). It is being drawn from the same place and moderated by the metal.
In the case of Feruchemy, no energy is being drawn from this other place. So, you spend a week sick and store up the ability to heal. It’s a balanced system, basically obeying the laws of thermodynamics. So, while it’s not real, it’s still rational.
In compounding, when you have the power of both Allomancy and Feruchemy, you draw power from the other place through the metal and it recognizes the power that is already stored—"Oh, this is healing, I know how to do that”—and so you get the power of Feruchemy but boosted by energy from the other place. This is how the Lord Ruler achieved immortality.