J. P. Crutchfield and D. P. Feldman, Statistical Complexity of Simple 1D Spin Systems, Physical Review E 55:2 (1997) 1239R-1243R.
We present exact results for two complementary measures of spatial structure generated by 1D spin systems with finite-range interactions. The first, excess entropy, measures the apparent spatial memory stored in configurations. The second, statistical complexity, measures the amount of memory needed to optimally predict the chain of spin values in configurations. These statistics capture distinct properties and are different from existing thermodynamic quantities.