[m_the0ry]

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However, there is nothing *fundamentally* wrong with fine-tuning a solution in such a way that for some small piece of the universe (one half of my space ship), the entropy is decreasing rather than increasing. It would merely be extremely difficult. If you did this by ordering the system just perfectly, you would still be obeying the 2nd law of thermodynamics, because in creating this order in the spaceship, you would disorder the rest of the universe

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So the force field only isolates the two halves of the ship, it doesn't make both halves of the ship closed systems. Like you said, in order for the decreasing entropy side to evolve the way it does and simultaneously obey the 2nd law, we have to continuously 'inject order' into the system.

I was making a pretty critical misinterpretation of your problem.

So the answer the original question, I think the increasing entropy side wins. To see why we have to envision the interactions not as 'running in -t time' but rather as going in +t time with the right conditions For each fusion reaction on the 'normal side', we have a fission reaction on the other side consisting of a perfectly synchronized meeting of one neutron, one helium, X gamma photons, and K joules of thermal energy. Especially when we consider the stochastic nature of the quantum world, this situation falls under the umbrella of 'technically feasible, astronomically improbable'. A question that comes to mind is whether it's possible to engineer a photon to be incident at such a specific time (order of femtoseconds?) and space (picometers) keeping in mind the uncertainty principle constraint. Which would make the entire process one that could only happen with a purely random 'order pump'.

Because every interaction with the backwards running half of the spaceship and its outside 'order injecting' system must be perfectly synchronized like this, any non-perfectly synchronized interaction would lead to a sort of cascade effect. But this depends on the behavior of the order pump. If we assume it keeps running and engineering ('chance-ineering?' is that even a word?) things to run in backwards physics then the question of 'who wins' is simply a matter of quantifying the order flux in the second half of the spaceship.