Islands in the stream of Hawking radiation

We consider the island formula for the entropy of subsets of the Hawking radiation in the adiabatic limit where the black hole evaporation is very slow. We find a simple concrete ‘on-shell’ formula for the generalized entropy which involves the image of the island out in the stream of radiation, the ‘island in the stream’. The resulting recipe for the entropy allows us to calculate the quantum information properties of the radiation and verify various constraints including the Araki-Lieb inequality and strong subadditivity.