Beyond the Holographic Entropy Cone via Cycle Flows

• URL: http://arxiv.org/abs/2312.10137v3
• Date: Sat, 12 Oct 2024 23:25:45 GMT
• Title: Beyond the Holographic Entropy Cone via Cycle Flows
• Authors: Temple He, Sergio Hernández-Cuenca, Cynthia Keeler,
• Abstract summary: We introduce a new prescription for computing entropy vectors outside the holographic entropy cone. We prove that the maximum cycle flow obeys both subadditivity and strong subadditivity. We conjecture that our model similarly generalizes the entropy vectors arising from hypergraphs.
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• Abstract: Motivated by bit threads, we introduce a new prescription for computing entropy vectors outside the holographic entropy cone. By utilizing cycle flows on directed graphs, we show that the maximum cycle flow associated to any subset of vertices, which corresponds to a subsystem, manifestly obeys purification symmetry. Furthermore, by restricting ourselves to a subclass of directed graphs, we prove that the maximum cycle flow obeys both subadditivity and strong subadditivity, thereby establishing it as a viable candidate for the entropy associated to the subsystem. Finally, we demonstrate how our model generalizes the entropy vectors obtainable via conventional flows in undirected graphs, as well as conjecture that our model similarly generalizes the entropy vectors arising from hypergraphs.

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