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I realize this is a thought experiment, but we call the second law a 'law' for a reason. As in, this is a rule that must be symmetric and invariant for the entire universe. Therefore I think you inherently must be describing two different universes, because their laws are different.

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Some people seem to be gravitating to this point, so let me say a couple things about the 2nd law.

Typical derivations of the 2nd law come from "course-graining" arguments. That is, you lump all states together that look more or less the same, and those correspond to the same "thermodynamic" state. The entropy then involves counting just how much wiggle room there is in each thermodynamic state -- how much could things be different, but still be the same thermodynamic state. And the 2nd law basically says things will tend to move randomly into thermodynamic states with more and more wiggle room (entropy). Thermodynamic equilibrium has by far the most wiggle room of any state -- once you get there, it's very improbable that you'll ever get out.

The problem is this: This argument works exactly the same if you evolve things backward in time. This comes from the fact that for EVERY solution that obeys the 2nd law, there is another one that violates it -- just time-reverse the solution (replace t by -t in the equations), and you get another perfectly good solution that solves the equations of motion.

So, from a fundamental statistical point of view, the 2nd law is just our universe moving toward higher entropy because it started in a state of very low entropy (perfectly reasonable and what the above argument predicts). 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 by a corresponding amount because it would take so much work to get everything "just right." (this happens in your computer, for example -- you order the hard drive and thus decrease it's entropy, but in doing so you increase the thermodynamic entropy of the universe by a corresponding amount -- this is why your computer gets hot)

So hopefully I've convinced everyone that this situation is not physically unthinkable -- merely insanely difficult or improbable. But once you have these systems (the hard part), it is amazing to me how difficult it is to describe what would happen when they are brought into contact -- even in the most rough, hand-waving sort of way (which should be the easy part). After thinking about this for way too long, I think I have most of it more or less sorted out -- still, it's amazing how fast it forces you confront fundamental issues in thermodynamics/stat mech.