Black-Hole Uncertainty Entails an Intrinsic Time Arrow. a Note on the   Hawking-Penrose Controversy
  Any theory that states that the basic laws of physics are time-symmetric must be strictly deterministic. Only determinism enables time reversal of entropy increase. A contradiction therefore arises between two statements of Hawking. A simulation of a system under time reversal shows how an intrinsic time arrow re-emerges, destroying the time reversal, when even slight failure of determinism occurs. 
Avshalom C. Elitzur and Shahar Dolev