  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.
