The entropy of Hawking radiation
Black holes have a temperature and an associated entropy. This thermodynamic entropy is equal to the area of their horizon.
Surprisingly, black holes have a second entropy, the von Neuman, fine grained, or quantum entropy which is given by the area of another surface. This entropy formula can be generalized to general systems involving gravity. When it is applied to radiation coming out of a black hole, it gives a result that suggests that black holes preserve information.