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Comment I on "Simple measure for complexity"

Crutchfield1, Feldman, Shalizi

  • 1Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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The Shiner, Davison, and Landsberg complexity measure is overly universal and incorrectly equates complexity with non-equilibrium states. Our critique demonstrates that structural complexity is independent of system equilibrium and disorder dependence.

Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • The Shiner, Davison, and Landsberg (1999) measure of complexity has been proposed for complex systems.
  • A key assumption in some complexity studies is its link to non-equilibrium dynamics.

Purpose of the Study:

  • To critique the universality of the Shiner, Davison, and Landsberg complexity measure.
  • To challenge the direct equivalence between complexity and non-equilibrium states.
  • To correct a previous misinterpretation of related research.

Main Methods:

  • Theoretical analysis of the Shiner, Davison, and Landsberg complexity measure.
  • Development of counterexamples to test the universality and equilibrium claims.
  • Re-evaluation of prior results on complexity and dynamics.

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Main Results:

  • The Shiner, Davison, and Landsberg complexity measure exhibits over-universality, showing identical disorder dependence across structurally distinct systems.
  • Counterexamples demonstrate that complex systems can exist at equilibrium, and simple systems can be out of equilibrium.
  • A misinterpretation of previous work by Crutchfield and Feldman (1997) is clarified.

Conclusions:

  • The proposed complexity measure's universality is questioned.
  • Complexity is not strictly synonymous with being out of equilibrium.
  • Structural complexity is a distinct property from a system's thermodynamic state.