Is there a measure of the universe's deviation from randomness?

[Loren Booda]

With so much structure and similarity in the cosmos, surely it must have some quantification of order. (I remember Alan Guth attributing a large but finite value to the universe's entropy in one of his first papers on inflation.) If the universe consists primarily of a relative handful of distinguishable particles, how far could it be from representation by absolute information (remembering J. A. Wheeler's "It from bit")?