Towards a Universal Measure of Complexity.

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.