Statistical Complexity of Simple 1D Spin Systems
James P. Crutchfield (University of California, Berkeley, Santa Fe, Institute), David P. Feldman (University of California, Davis)
TL;DR
This paper provides exact calculations of two measures, excess entropy and statistical complexity, to analyze the spatial structure and memory in simple one-dimensional spin systems with finite-range interactions.
Contribution
It introduces exact results for excess entropy and statistical complexity in 1D spin systems, highlighting their distinct properties from thermodynamic quantities.
Findings
Exact expressions for excess entropy and statistical complexity.
Demonstrates these measures capture different aspects of spatial structure.
Provides insights into the memory properties of 1D spin configurations.
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. These statistics capture distinct properties and are different from existing thermodynamic quantities.
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