A quantitative measure, mechanism and attractor for self-organization in networked complex systems

TL;DR

This paper introduces a quantitative measure of organization in complex networks based on physical action, identifies a mechanism for self-organization as action minimization, and describes an attractor state for system evolution.

Contribution

It proposes a universal measure of organization in complex systems and links self-organization to the minimization of physical action, providing a new theoretical framework.

Findings

Self-organization decreases average action per element.

The lowest action state acts as an attractor for system evolution.

Increasing elements accelerates self-organization through grouping.

Abstract

Quantity of organization in complex networks here is measured as the inverse of the average sum of physical actions of all elements per unit motion multiplied by the Planck's constant. The meaning of quantity of organization is the inverse of the number of quanta of action per one unit motion of an element. This definition can be applied to the organization of any complex system. Systems self-organize to decrease the average action per element per unit motion. This lowest action state is the attractor for the continuous self-organization and evolution of a dynamical complex system. Constraints increase this average action and constraint minimization by the elements is a basic mechanism for action minimization. Increase of quantity of elements in a network, leads to faster constraint minimization through grouping, decrease of average action per element and motion and therefore accelerated rate of self-organization. Progressive development, as self-organization, is a process of minimization of action.