Structural Complexity as a Directional Signature of System Evolution: Beyond Entropy.

Area of Science:

• Complexity Science
• Thermodynamics
• Information Theory

Background:

• Traditional entropy measures are limited to closed, equilibrium systems.
• Understanding system evolution in open, non-equilibrium systems requires new metrics.
• Schrödinger's concept of biological growth locally reducing entropy while increasing order provides a basis.

Purpose of the Study:

• To propose a universal framework for system evolution based on structural complexity.
• To introduce quantifiable metrics for organized complexity in open systems.
• To formalize a new Universal Law for system evolution.

Main Methods:

• Utilizing Kolmogorov Complexity (KC) to measure algorithmic complexity.
• Employing Fractal Dimension (FD) to quantify geometric complexity.
• Developing a non-decreasing function Ω(t) = α·KC(t) + β·FD(t) to model system evolution.

Main Results:

• KC and FD provide scalable metrics for organized complexity in open, non-equilibrium systems.
• The proposed Universal Law, Ω(t), parallels the Second Law of Thermodynamics but tracks algorithmic and geometric complexity.
• The framework applies across physical, chemical, and biological domains.

Conclusions:

• The proposed framework offers a directional signature for system evolution applicable across diverse scientific domains.
• This approach integrates complexity science principles for a mathematically grounded understanding of system development.
• The framework provides a novel lens for describing directional evolution from simple structures to complex cognition.