| J. P. Crutchfield Physics Department University of California Berkeley, California 94720-7300, USA and Santa Fe Institute 1399 Hyde Park Rd. Santa Fe, NM 87501, USA |
David P. Feldman Department of Physics University of California Davis, California 95616, USA |
ABSTRACT: 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.