It looks like Zurek figured out the answer some time ago. The answer is that the end entropy is ~4/3 times the initial entropy.
For anyone else interested in this, see W. H. Zurek, Phys. Rev. Lett. 49 1683 (1982).
I am a little confused over something, so perhaps someone can tell me which one of the following statements is incorrect. (I don't know a lot about this, so forgive my ignorance).
Suppose that we have a closed system of some size, and we start in a state where we have a black hole at the...