Time dependence of entanglement for steady state formation in AdS$_3$/CFT$_2$

TL;DR

This paper studies the time evolution of entanglement entropy in a holographic model of two heat baths at different temperatures, revealing bounds on entanglement growth and validating entanglement inequalities during steady state formation.

Contribution

It introduces a method to compute time-dependent entanglement entropy holographically in a dynamic setup with heat baths at different temperatures.

Findings

Entanglement entropy growth rate obeys known bounds.

Non-trivial entanglement inequalities hold during steady state formation.

Holographic model captures causal structure and entanglement dynamics.

Abstract

We consider a holographic model of two 1+1-dimensional heat baths at different temperatures joined at time $t=0$, such that a steady state heat-current region forms and expands in space for times $t>0$. After commenting on the causal structure of the dual 2+1-dimensional spacetime, we present how to calculate the time-dependent entanglement entropy of the boundary system holographically. We observe that the increase rate of the entanglement entropy satisfies certain bounds known from the literature on entanglement tsunamis. Furthermore, we check the validity of several non-trivial entanglement inequalities in this dynamic system.