The Least Action and the Metric of an Organized System

TL;DR

This paper formulates a principle for organized systems based on minimizing total action, linking physical laws to system organization through metrics and exploring both closed and open systems.

Contribution

It introduces a novel formulation of the Least Action Principle for organized systems and connects the metric tensor to system organization, providing dual measures of development.

Findings

The least action principle applies to organized systems.

The metric tensor describes the system's constraints and organization.

Organization levels are quantified by action and metric tensor.

Abstract

In this paper we formulate the Least Action Principle for an Organized System as the minimum of the total sum of the actions of all of the elements. This allows us to see how this most basic law of physics determines the development of the system towards states with less action - organized states. Also we state that the metric tensor can describe the specific state of the constraints of the system, which is its actual organization. With this the organization is defined in two ways: 1. A quantitative: the action I. 2. A qualitative: the metric tensor. These two measures can describe the level of development and the specifics of the organization of a system. We consider closed and open systems.