Could a very small black hole where half of its entropy has been radiated, emit Hawking radiation that is macroscopically distinct from being thermal? i.e: not a black body radiator. Or would the scrambling property mean that the initial states that produce the non-thermal Hawking radiation are micro states that are macroscopically indistinguishable from micro states that lead to Hawking radiation that is nearly thermal?
For the sake of the question, if two microscopic states are macroscopically indistinguishable, it should be assumed that preparing the state in one or the other is physically impossible, even if it is possible in principle.
a reference to a recent TRF post about thermal and pure states of black holes being macroscopically indistinguishable from the outside