Quantifying system order for full and partial coarse graining

We show that Fisher information I and its weighted versions effectively measure the order R of a large class of shift-invariant physical systems. This result follows from the assumption that R decreases under small perturbations caused by a coarse graining of the system. The form found for R is generally unitless, which allows the order for different phenomena to be compared objectively. The monotonic contraction properties of R and I in time imply that they are entropies, in addition to their usual status as information. This removes the need for data, and therefore an observer, in physical derivations based upon their use. Thus, this recognizes complementary scenarios to the participatory observer of Wheeler, where (now) physical phenomena can occur in the absence of an observer. Simple applications of the new order measure R are discussed.