Quantum entanglement, two-sided spacetimes and the thermodynamic arrow of time

TL;DR

This paper explores how quantum entanglement between two CFTs influences the thermodynamic arrow of time and the structure of dual spacetimes in the AdS/CFT correspondence, linking entanglement to spacetime connectivity.

Contribution

It introduces a novel connection between entanglement in dual CFTs and the geometric sidedness of the corresponding spacetime in AdS/CFT, highlighting how entanglement affects the thermodynamic arrow of time.

Findings

Uncorrelated CFTs lead to a definite thermodynamic arrow of time with increasing entropy.

High correlation allows entropy to both increase and decrease, removing a preferred time direction.

Maximal entanglement correlates with a connected, one-sided spacetime in the dual gravity description.

Abstract

We investigate the emergence of thermodynamic arrow of time in the context of AdS/CFT correspondence. We show that, on the CFT side, if the two copies of the field theory are not initially correlated the entropy can only increase such that a definite orientation for the thermodynamic arrow of time is imposed. Conversely, in a high-correlation environment, the entropy can either increase or decrease, such that there is no opportunity for the dominance of one direction of time over the other. On the gravity side, we construct the structure of geometric dual by considering the notion of spacetime sidedness and time-orientability. Accordingly, we conjecture that the entanglement of the CFTs in the thermofield double state, impose the connection of the two sides of the spacetime forming a one sided spacetime. In addition, disentangling the degrees of freedom of the two CFTs, results in disconnecting the two sides of the spacetime. In essence, the maximal entanglement between the two copies of CFT builds, in the geometric dual, a connection between the two sides of spacetime.