I have a question about applying posets into resource theories.
How would you translate the reflexive property \\(x \leq x\\) in a resource theoretic way?
The natural way for me to read it is "what goes in must come out" and ties in nicely with the impossibility of 100% yield in reality. Even processes that seemingly have 100% yield are microscopically less than 100% due to entropy. In the lemon pie example, even if you think you use all the butter you can really never use all the butter since there will be remnants left on everything you use to touch it which ends up going out as waste.
Is this a valid line of reasoning?
If it is, then when people assume 100% yield like when you ignore by products, this would no longer be a preorder since reflexivity is disobeyed?