[joe_the_user]

Given that according to quantum mechanics, empty space continually experiences small, random fluctuations[1], I think you can argue that in the normal space, information does on average expand proportionally to the volume encompassed, even if the proportionality constant is rather low (edit: this applies to space-time volume too since the fluctuations are random, distinct on each timeslice).

Indeed, I think quantum mechanics would be the only system that guarantees this. I suppose a purely classical system that was entirely reversible couldn't contain information in the time dimension because each moment would imply every other moment. But claiming that any system determined by classical differential equations is "holographic" might be a stretch.

[1] http://en.wikipedia.org/wiki/Quantum_fluctuation