Increase of Organization in Complex Systems

TL;DR

This paper introduces a new measure of organization in complex systems based on the principle of least action, demonstrating its application to CPU evolution and its potential for broad interdisciplinary use.

Contribution

It proposes a novel quantitative measure of organization rooted in physics, applicable across various complex systems to analyze self-organization and evolution.

Findings

Organization in CPUs follows a double exponential growth pattern.

The measure reveals an S-shaped functional dependence indicating mechanisms of self-organization.

The approach explains how systems increase organization through action minimization and constraints.

Abstract

Measures of complexity and entropy have not converged to a single quantitative description of levels of organization of complex systems. The need for such a measure is increasingly necessary in all disciplines studying complex systems. To address this problem, starting from the most fundamental principle in Physics, here a new measure for quantity of organization and rate of self-organization in complex systems based on the principle of least (stationary) action is applied to a model system - the central processing unit (CPU) of computers. The quantity of organization for several generations of CPUs shows a double exponential rate of change of organization with time. The exact functional dependence has a fine, S-shaped structure, revealing some of the mechanisms of self-organization. The principle of least action helps to explain the mechanism of increase of organization through quantity accumulation and constraint and curvature minimization with an attractor, the least average sum of actions of all elements and for all motions. This approach can help describe, quantify, measure, manage, design and predict future behavior of complex systems to achieve the highest rates of self organization to improve their quality. It can be applied to other complex systems from Physics, Chemistry, Biology, Ecology, Economics, Cities, network theory and others where complex systems are present.