# Membrane theory of entanglement dynamics The **membrane theory** is an effective model designed to describe [[0522 Entanglement dynamics|entanglement dynamics]]. It captures more information than the [[0518 Quasiparticle model|quasiparticle model]]. In this model, the [[0301 Entanglement entropy|entanglement entropy]] is given by $S=s_{\mathrm{th}} \int d^{d-1} y \sqrt{-\gamma} \frac{\mathcal{E}(v)}{\sqrt{1-v^2}},$where $\mathcal{E}(v)$ is a *tension* that depends on the instantaneous velocity (or "angle") of the timelike membrane stretching between two constant-time slices of Minkowski spacetime. At this point, nothing is holographic yet. Using holography, this model can be formulated using [[0007 RT surface|HRT]] surfaces. ## Refs - [[2018#Jonay, Huse, Nahum]] - 2d unitary random evolution - conjecture of minimal membrane description of entanglement dynamics of large regions in generic chaotic systems - [[2018#Mezei]] - holographic proof - arbitrary dimensions - [[2019#Agon, Mezei]] - reformulation using [[0211 Bit thread|bit threads]] - [[2019#Mezei, Virrueta (Dec)]] - generalisations (including [[0006 Higher-derivative gravity|HDG]] corrections, more general initial states, joining quenches, etc) - contains a nice review of earlier work - [[2023#Rampp, Rather, Claeys]] - calculation in an exactly solvable model - [[2024#Vardhan, Moudgalya]] - Renyi entropy, universal low lying modes - [[2024#Jiang, Mezei, Virrueta]] - 2d CFT ## Membrane tension - [[0327 Entanglement velocity|entanglement velocity]] - $\mathcal{E}(0)=v_E$ - [[0167 Butterfly velocity|butterfly velocity]] - $\mathcal{E}\left(v_B\right)=v_B$ - $\mathcal{E}^{\prime}\left(v_B\right)=1$