Emergent spacetime and the ergodic hierarchy

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>III</a:mi></a:mrow><a:mrow><a:mn>1</a:mn></a:mrow></a:msub></a:mrow></a:math> von Neumann algebras carrying half-sided modular inclusions. This Letter 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. Published by the American Physical Society 2024

Topics & Concepts