  We consider quantum algebras of observables associated with subregions in
theories of Einstein gravity coupled to matter in the $G_N\rightarrow 0$ limit.
When the subregion is spatially compact or encompasses an asymptotic boundary,
we argue that the algebra is a type II von Neumann factor. To do so in the
former case we introduce a model of an observer living in the region; in the
latter, the ADM Hamiltonian effectively serves as an observer. In both cases
the entropy of states on which this algebra acts is UV finite, and we find that
it agrees, up to a state-independent constant, with the generalized entropy.
For spatially compact regions the algebra is type II$_1$, implying the
existence of an entropy maximizing state, which realizes a version of
Jacobson's entanglement equilibrium hypothesis. The construction relies on the
existence of well-motivated but conjectural states whose modular flow is
geometric at an instant in time. Our results generalize the recent work of
Chandrasekaran, Longo, Penington, and Witten on an algebra of operators for the
static patch of de Sitter space.
