Asymptotic and Catalytic Resource Orderings: Beyond Majorization

This talk is a progress report on ongoing research. I will explain what resource theories have to do with real algebraic geometry, and then present a preliminary result in real algebraic geometry which can be interpreted as a theorem on asymptotic and catalytic resource orderings.

It reproves the known criterion for asymptotic and catalytic majorization in terms of Rényi entropies, and generalizes it to any resource theory which satisfies a mild boundedness hypothesis. I will sketch the case of matrix majorization as an example.