Entanglement Entropy and Mutual Information Production Rates in Acoustic Black Holes

TL;DR

This paper proposes a method to measure entanglement entropy and mutual information in acoustic black holes, confirming theoretical predictions with analytical analysis of 1D Fermi fluid flows.

Contribution

It introduces a novel approach to investigate acoustic Hawking radiation through entropy and mutual information measurements, validated by analytical calculations.

Findings

Entropy production rate is proportional to sound acceleration, 

Mutual information formation ensures information conservation

Analytical results match theoretical predictions in 1D Fermi flows

Abstract

A method to investigate acoustic Hawking radiation is proposed, where entanglement entropy and mutual information are measured from the fluctuations of the number of particles. The rate of entropy radiated per one-dimensional (1D) channel is given by $\dot{S}=\kappa/12$, where $\kappa$ is the sound acceleration on the sonic horizon. This entropy production is accompanied by a corresponding formation of mutual information to ensure the overall conservation of information. The predictions are confirmed using an \emph{ab initio} analytical approach in transonic flows of 1D degenerate ideal Fermi fluids.