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Towards a Universal Measure of Complexity.

Jarosław Klamut1, Ryszard Kutner1, Zbigniew R Struzik1,2,3

  • 1Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland.

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This study challenges the idea that entropy directly measures complexity. It proposes a new universal complexity measure based on Gell-Mann

Keywords:
dynamical complexityentropic susceptibilitiesentropiesirreversible processesuniversal complexity measure

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Area of Science:

  • * Physics
  • * Information Theory
  • * Complex Systems

Background:

  • * Current understanding posits entropy as a direct complexity measure.
  • * This view suggests lower entropy equals lower complexity and higher entropy equals higher complexity.
  • * This study disputes this direct relationship.

Purpose of the Study:

  • * To propose a universal measure of complexity.
  • * To challenge the direct entropy-complexity relationship.
  • * To introduce a complexity measure based on Gell-Mann's perspective.

Main Methods:

  • * Non-linear transformation of time-dependent entropy.
  • * Defining complexity based on distance from less complex states.
  • * Utilizing a paradigmatic example with varying degrees of freedom.

Main Results:

  • * A universal complexity measure is proposed.
  • * The most complex state is identified as an optimally mixed state.
  • * This state balances regularity and disorder within the system's state space.

Conclusions:

  • * Entropy is not a direct measure of complexity.
  • * The proposed universal measure offers flexibility and suitability for analyzing critical behavior and dynamic complexity.
  • * The optimally mixed state represents the peak of complexity.