to calculate the thermodynamical entropy, I suppose that you could use the famous Boltzmann entropy equation:
S=k*ln W
W is the number of distinguishable arrangements of atoms/molecules.
If you are able to figure out W, work done!
The entropy of a black hole is [tex]S=\frac{Akc^3}{4hG}[/tex] where A is the area of the black hole, k the Boltzmann's constant, h the Planck's constant, c the speed of light and G the gravitational constant
(http://nrumiano.free.fr/Estars/bh_thermo.html)
I'm not sure you can use the same formula for a (neutron) star though.