Abstract: Twisted van der Waals materials provide a new venue to explore flat electronic bands and the interaction-driven states they host. While many such phases have been reported, little is known about their excitations or how they depend on externally applied fields. In this talk, I will present two examples where electronic compressibility measurements with a scanning single-electron transistor clarify the nature of correlated ground states and allow us to identify their nontrivial excitations. In magic-angle graphene, we observe thermodynamic gaps at zero magnetic field whose non-monotonic dependence on field is indicative of spin skyrmions. I will also describe measurements of twisted double bilayer WSe2, which realizes a triangular Hubbard lattice that supports spin polaron excitations at low field. I will discuss how local thermodynamic measurements can yield unique insight into these novel states and the microscopic parameters that stabilize them.