The concept of an order and its application for research of the deterministic chains of symbols

TL;DR

This paper introduces a new concept of order for highly organized systems, proposing an alternative to entropy, and applies it to analyze non-random binary sequences, exploring properties of an order parameter.

Contribution

It presents a novel framework for measuring system order using order poles and defines an order parameter for binary sequences, expanding beyond classical information measures.

Findings

Defined the concept of order poles and order parameters.

Compared the new order measure to classical information entropy.

Analyzed properties of the order parameter in binary sequences.

Abstract

The present work is dedicated to searching parameters, alternative to entropy, applicable for description of highly organized systems. The general concept has been offered, in which the system complexity and order are functions of the order establishment rules. The concept of order poles has been introduced. The concept is being applied to definition of the order parameter (OP) for non-random sequences with equal number of zeros and ones. Properties of the OP are being studied. Definition of the OP is being compared to classical definition of amount of information.