I was trying to think but cannot figure it out. For instance, if the interaction is small, for instance limited to a windows, the observers in each universe will see that the other goes in reverse. But what if they can start a more meaningful interaction? (for instance, if one observer crosses the window and moves to the other universe, will anything change? why and how fast? (at least at the beginning his thinking will move in the same time arrow than in his universe, but the physical processes around him will still violate the second law?
Answer
Based on the article by Kupervasser suggested in the comments by Ben Crowell, I suspect the answer is that my hypothetical situation is impossible: in general, for a complex enough dynamical system, there is no solution to the equations is which two universes with opposite arrows of time can interact. In order to have that, your system should have to satisfy boundary condition of low entropy for both universes at their beginnings, which are most likely impossible to satisfy (that is, you must satisfy initial conditions for half of your system and final conditions for the other half, which is in most cases mathematically impossible).
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