There's a fun thermodynamic argument that does not fit in the margins of this hacker news explaining why you can not transmit information by lowering entropy on something already in its ground state.
As for transferring information in general, see "light cones". Going forwards you can't send info further away than the speed of light would reach, and going backwards there isn't much of a light cone...
This prevents information from being stored inside the system, but does not prevent the system from being used "in bulk" as information storage. Crude analogy is you could make a Turing machine where "mark" equals drop one of these crystals on the tape "space" equals wipe it off or flip it upside down or whatever. Or you could make essentially a punchcard by building a 10x10 array of them and smashing some of them in a pattern... theoretically the unsmashed ones would never ever decay, and the smashed ones are too complicated to spontaneously reform, so a large collection of them aligned in certain patterns would actually make a pretty decent ultra long term storage media.