Entanglement Entropy and Mutual Information Production Rates in Acoustic Black Holes

Understand

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.