Two particles floating in space, with a given energy, have a given amount of entropy and therefore information. The entropy is the logarithm of the number of states available to them at that energy; if they move further apart, that is a conversion of kinetic to potential energy (I'm assuming they interact gravitationally, but other forces do not change the argument) which is already accounted for in the entropy. Therefore, no, the distance is not an additional piece of information, it has been counted in the number of possible states. You can only change the entropy by adding energy - this is equivalent to adding mass; I've been simplifying by saying 'mass' throughout.

As for discoveries in physics: I do not wish to say that this is impossible. But it would require new understandings in statistical mechanics and thermodynamics, which are by this point really well understood. You're talking about something rather more unlikely than overthrowing general relativity, here; we know GR doesn't work at all scales. In any case, I can only update on information I already have; if you bring in New Physics, you can justify anything.