Does anti-matter increase or decrease in entropy over time? Antimatter is matter going backwards through time. From the perspective of a matter-based observer does antimatter:


*

*Increase in entropy (and therefore decrease in entropy in its own time)


OR


*

*Decrease in entropy (and therefore increase in entropy in its own time)


Option 2 would seem to explain why we don't see much anti-matter (it all went into energy.)
Which is correct? Does antimatter increase or decrease in entropy over time?
 A: Antimatter increase in entropy over time. We can verify this with a thought experiment. Take ten positrons. Put five in one side of a chamber with a barrier and then the other 5 on the other side of the barrier in the same chamber. The chamber and barrier are also made of antimatter. The positrons repel each other and so each have a certain amount of kinetic energy due to changes in their potential energy. Now, remove the barrier and see if they tend to randomly assort themselves throughout the chamber. Because they are more likely to be found in disordered arrangements over time we know that the entropy of this system is increasing with time. 
What we wouldn't observe, is all of the positrons moving back to where they started and not mixing at all. Not that it's impossible, just extremely unlikely.
A: 
Antimatter is matter going backwards through time. 

No it isn't. Whilst that idea might appear to have some pedigree, (see retrocausality on Wikipedia), it's bunk I'm afraid. Antimatter is like matter, but it has the opposite chirality. Google on positron chirality. Whilst one can mathematically model the positron as a "time reversed electron", it isn't actually going backwards through time. It's more like it has the opposite spin. And charge. Have a look at the picture of a spinor here. It's essentially a Möbius strip, which is chiral. It has a handedness. If you go round the strip one way, it has a clockwise rotation. That's like matter. If you go round it backwards, it has an anticlockwise rotation. That's like antimatter. There is a sense wherein antimatter is "matter going backwards", but not through time.       

From a matter-based observer does antimatter:
  •Increase in entropy (and therefore decrease in entropy in its own time)
  OR
  •Decrease in entropy (and therefore increase in entropy in its own time(

It increases, just like matter. Like what Alex said. 

Option 2 would seem to explain why we don't see much anti-matter (it all went into energy).

It doesn't I'm afraid. 
A: The answers given are speculative, as the answer to your question is unknown. The thermodynamics of antimatter is an open question in physics, and future experimentation will be required to reach a definitive answer. If CPT (charge, parity, time) symmetry is true, then antimatter would be expected to behave has though time is reversed, that is if we observed a system of only antimatter it would appear as though its entropy change over time was strictly less than or equal to zero.
