The mathematics of resource efficiency

I will sketch how analogous structures involving resource efficiency come up in various contexts, including chemistry, information theory, thermodynamics, and the mixing of paint. The general mathematical theory behind this is the theory of ordered commutative monoids. Among the main tools provided by this theory is a characterization of asymptotic efficiency in terms of monotone functionals, with a potential strengthening to monotone semiring homomorphisms via a suitable Positivstellensatz from real algebraic geometry. I will explain inner-mathematical applications to asymptotic aspects of graph theory, representation theory, and majorization theory.