  We explore nonequilibrium features of certain operator algebras which appear
in quantum gravity. The algebra of observables in a black hole background is a
Type $\mathrm{II}_\infty$ von Neumann algebra. We discuss how this algebra can
be coupled to the algebra of observable of an infinite reservoir within the
canonical ensemble, aiming to induce nonequilibrium dynamics. The resulting
dynamics can lead the system towards a nonequilibrium steady state which can be
characterized through modular theory. Within this framework we address the
definition of entropy production and its relationship to relative entropy,
alongside exploring other applications.
