1997/08/22 by David P. Feldman, James P. Crutchfield, Feldman, David P. +1
Computer Science · Decision Sciences · #Adaptation and Self-Organizing Systems (nlin.AO) #Complex Systems and Decision Making #Computational Drug Discovery Methods #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.cond-mat/9708186
openalex publication_date 1997/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We review several statistical complexity measures proposed over the last decade and a half as general indicators of structure or correlation. Recently, Lopez-Ruiz, Mancini, and Calbet [Phys. Lett. A 209 (1995) 321] introduced another measure of statistical complexity CLMC that, like others, satisfies the ``boundary conditions'' of vanishing in the extreme ordered and disordered limits. We examine some properties of CLMC and find that it is neither an intensive nor an extensive thermodynamic variable and that it vanishes exponentially in the thermodynamic limit for all one-dimensional finite-range spin systems. We propose a simple alteration of CLMC that renders it extensive. However, this remedy results in a quantity that is a trivial function of the entropy density and hence of no use as a measure of structure or memory. We conclude by suggesting that a useful ``statistical complexity'' must not only obey the ordered-random boundary conditions of vanishing, it must also be defined in a setting that gives a clear interpretation to what structures are quantified.