Emergent spacetime and the ergodic hierarchy

• URL: http://arxiv.org/abs/2310.13733v1
• Date: Fri, 20 Oct 2023 18:00:00 GMT
• Title: Emergent spacetime and the ergodic hierarchy
• Abstract summary: The emergence of an arrow of time in the bulk description of a holographic theory has been proposed. This note puts forward a close parallel between these diagnostics and a quantum formulation of the ergodic hierarchy of dynamical systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Various diagnostics of the emergence of an arrow of time in the bulk description of a holographic theory have been proposed, including the decay of some real time correlation functions and the appearance of type III$_1$ von Neumann algebras carrying half-sided modular inclusions. This note puts forward a close parallel between these diagnostics and a quantum formulation of the ergodic hierarchy of dynamical systems. Theories with an emergent spacetime appear to sit near the top of this hierarchy.

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