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I agree that the energy must balance. In the real world, the leakages of energy from the system would mean that in reality to need to put more energy in than you got out, because some of the energy you obtained was leaked out of the system. In this gedankenexperiment we are assuming no leakage.Ofcourse, the fact that you will obtain as much energy out of the combustion as you will put into the disassociation does not mean you will not need more on a transient basis to trigger the disassociation, even if that extra is energy is later recovered.I think the probability that all of the water will disassociate into hydrogen and oxygen is highly improbably small, but arguable probably non-zero; but the reality will be that some proportion of the water will continually be disassociating. The issues that are going to matter are the ambient temperature and pressure, and how evenly the energy is distributed in the box, because you will need enough energy in any one locality in order to feed the disassociation process in that locality, but any energy in one region would have to mean less energy in another region, and so less likelihood that there will be sufficient energy elsewhere to drive disassociation.
The vast majority of the photons will have much lower energy than is required to cause dissociation of the H and O atoms (the specific frequency which was produced during combination) so the H2O molecules will stay as H2O.
I'll just shut up then 
we have not been given enough information to say it is so. We have been told that no energy can leek in or out of the box, but we have not been told how much energy was initially in the box
What does this mean for entropy?