Abstract: Integrating out degrees of freedom and studying the universality of thus obtained effective field theories is a standard and powerful tool for analyzing QFTs. There are several ways to generalize this procedure to theories without a useful product structure in the Hilbert space, such as ordinary quantum mechanics, the SYK model, or QFTs with global constraints. I will discuss two such methods in this talk: an operator approach that provides a useful handle on quantum ergodicity, and a real-time path integral approach that displays some surprising connections to gravity.