[Metric]

This is close to my own interpretation, except that:

1) I do not think of it in terms of a "continuous order pump" -- merely a stupendously ordered set of initial conditions, which would only be required in one half of the ship. The other side could have generic initial conditions. The side with generic initial conditions then wins the "collision of time's arrows."

2) There is another way to phrase the problem, in terms of "generic initial conditions" in half A, and "generic final conditions" in half B (which, given the backward evolution in half B are really a kind of initial condition for B). This is the most time symmetric form of the problem, in which you can't really state which is the "correct" arrow of time by appealing to the outside. In this case, the thermodynamic future of both sides appears to me to pretty much be destroyed.