Fox and Hedgehog Seminar Series - 'A category theorist thinks about entropy'

Category theorists love pointing at some important concept from another branch of mathematics or science and saying "it's just a ...", where the rest of the sentence will involve some word like "universal", "functor" or "adjoint". This can be clarifying for both the subject at hand and its relationship with other subjects. Now, entropy is very important in physics, mathematics and beyond, but it's not obvious how to understand it categorically. I haven't got to the bottom of this question either, but I will tell a surprising story that brings together various types of entropy, category theory, analysis, geometry, and even some theoretical ecology.