Statistical Complexity of Simple 1D Spin Systems

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

and

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.

Citation

J. P. Crutchfield and D. P. Feldman, Statistical Complexity of Simple 1D Spin Systems, Physical Review E 55:2 (1997) 1239R-1243R.

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