# Holographic Entropy Cone with Time Dependence in Two Dimensions

## TL;DR

This paper demonstrates that in two-dimensional holographic systems, all entanglement entropy inequalities valid in static geometries also hold in time-dependent cases, extending the holographic entropy cone to dynamic scenarios.

## Contribution

It proves that entropy inequalities established for static holographic geometries also apply to time-dependent states in two-dimensional holography using kinematic space techniques.

## Key findings

- All static entropy inequalities hold in time-dependent cases in 2D holography.
- Kinematic space methods effectively extend static results to dynamic settings.
- The holographic entropy cone remains valid under time evolution in the studied context.

## Abstract

In holographic duality, if a boundary state has a geometric description that realizes the Ryu-Takayanagi proposal then its entanglement entropies must obey certain inequalities that together define the so-called holographic entropy cone. A large family of such inequalities have been proven under the assumption that the bulk geometry is static, using a method involving contraction maps. By using kinematic space techniques, we show that in two boundary (three bulk) dimensions, all entropy inequalities that can be proven in the static case by contraction maps must also hold in holographic states with time dependence.