Bit Threads and the Membrane Theory of Entanglement Dynamics

Abstract

Recently, an effective {\it membrane theory} was proposed that describes the ``hydrodynamic'' regime of the entanglement dynamics for general chaotic systems. Motivated by the new {\it bit threads} formulation of holographic entanglement entropy, given in terms of a convex optimization problem based on flow maximization, or equivalently tight packing of bit threads, we reformulate the membrane theory as a max flow problem by proving a max flow-min cut theorem. In the context of holography, we explain the relation between the max flow program dual to the membrane theory and the max flow program dual to the holographic surface extremization prescription by providing an explicit map from the membrane to the bulk, and derive the former from the latter in the ``hydrodynamic'' regime without reference to minimal surfaces or membranes.

31 pages, 8 figures; v2: Improved figures, references added, a new discussion section was included, matches the published version

References in corpus (10)

• Geometric Aspects of Holographic Bit Threads
• Riemannian and Lorentzian flow-cut theorems
• Membrane theory of entanglement dynamics from holography
• Bit Threads and Holographic Monogamy
• Bit threads and holographic entanglement of purification
• Bulk locality and cooperative flows
• Bit threads and holographic entanglement of purification
• Bit Threads in Higher Curvature Gravity
• Coarse-grained dynamics of operator and state entanglement
• On the Entropy Cone for Large Regions at Late Times

Cited by in corpus (6)

• The entanglement membrane in chaotic many-body systems
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• Can the Macroscopic Fluctuation Theory be Quantized?
• Inequalities of Holographic Entanglement of Purification from Bit Threads
• Quantum bit threads and holographic entanglement
• Entanglement entropy in cubic gravitational theories