A manifestation of the black hole information loss problem is that the two-point function of probe operators in an eternal AdS black hole decays exponentially fast in time, whereas, on the boundary, it is expected to be an almost periodic function of time. We point out that the decay of the two-point function (clustering in time) holds important clues to the nature of observable algebras, states, and dynamics in quantum gravity. In the thermodynamic limit of infinite entropy (infinite volume or large N), the operators that cluster in time are expected to form an algebra. We prove that this algebra is a unique and very special infinite dimensional algebra called the III_1 factor. This has implications for the emergence of a local bulk in holography.
An important example is \mathcal{N}=4 SYM, above the Hawking-Page phase transition. The clustering of the single trace operators implies that the algebra is a type III_1 factor. We prove a generalization of a conjecture of Leutheusser and Liu to arbitrary out-of-equilibrium states. We explicitly construct the C^*-algebra and von Neumann subalgebras associated with time bands and more generally, arbitrary open sets of the bulk spacetime in the strict N\to \infty limit. The emergence of time algebras is intimately tied to the second law of thermodynamics and the emergence of an arrow of time.