If you assume that based on the laws of conservation of mass and energy, information cannot decay into a nonexistent state, then if the dark matter of one galaxy collided with the dark matter of another galaxy, the one with more dark matter (aka more "information" in this example) would be subject to less overall decay due to having more energy available during the collision, or perhaps would even absorb the structure of the lower-entropy dark matter. I realise I brought up entropy here and it may not seem relevant but if information is really structured in the universe then maybe entropy is what dictates the interactions like what you described above.