Marius - your [remarks on catalysis]( are very interesting and important! One of the beauties of resource theory is that it lets us make the concept of "catalyst" very general and mathematical.

In [Lecture 20](, I talk about some reactions in manufacturing, like these:

$$ \textrm{[processing chip]} + \textrm{[memory chip]} + 4 \textrm{[minute]} \to \textrm{[laptop]} $$

$$ \textrm{[processing chip]} + 2 \textrm{[memory chip]} + 3 \textrm{[minute]} \to \textrm{[desktop]} $$

$$ \textrm{[laptop]} \to 750\textrm{[profit]} $$

$$ \textrm{[desktop]} \to 1000 \textrm{[profit]} $$

These are often studied using linear programming. Linear programming _ignores catalysis_ because it doesn't distinguish between a reaction, say

$$ X + Y \to Z, $$

and a similar reaction that involves a catalyst:

$$ X + Y + C \to Z + C. $$

The manufacturing reactions I listed don't involve catalysis, but if they did, linear programming would be somewhat inadequate to capture all the details! (At least the simple sort of linear programming I know about. Maybe there's a fancier version that handles catalysis.)