  We study the algebra of observables in semiclassical quantum gravity for
cosmological backgrounds, focusing on two key examples: slow-roll inflation and
evaporating Schwarzschild-de Sitter black holes. In both cases, we demonstrate
the existence of a nontrivial algebra of diffeomorphism-invariant observables
\emph{without} the introduction of an external clock system or the presence of
any asymptotic gravitational charges. Instead, the rolling inflaton field and
the evaporating black hole act as physical clocks that allow a definition of
gauge-invariant observables at $G = 0$. The resulting algebras are both Type
II$_\infty$ factors, but neither is manifestly a crossed product algebra. We
establish a connection between the Type II entropy of these algebras and
generalized entropies for appropriate states. Our work extends previous results
on Type II gravitational algebras and highlights the crucial role of
out-of-equilibrium dynamics for defining gauge-invariant observables in
semiclassical canonically quantised gravity. We also briefly discuss the
construction of gauge-invariant algebras for compact wedges bounded by extremal
surfaces in generic spacetimes (i.e. in the absence of any Killing symmetry).
In contrast to the inflaton and black hole cases, this algebra does end up
being a simple crossed product. No clock or asymptotic charges are required
because of the absence of any symmetry in the classical background.
