Energy correlations are infrared-safe observables in QCD, which are relevant for studying jets and precision collider physics. There have been significant theoretical advancements in recent years regarding the analytic calculation of these observables. Many of these advancements are inspired by the representation of energy correlations as integrated correlation functions of composite operators. In particular, this approach has allowed for the analytic calculation of event shapes at high orders of perturbation theory in maximally supersymmetric Yang-Mills theory and a detailed study of their collinear asymptotics in QCD. In this talk, we will discuss energy correlations in states created by a heavy operator of the maximally supersymmetric Yang-Mills theory. The energy correlations in such states exhibit two regimes as functions of the angular separations between the calorimeters, and the transition between them is controlled by the dimension of the heavy operator and the dynamics of the theory. The talk is based on joint work with Gregory Korchemsky, Emery Sokatchev, and Alexander Zhiboedov.