# Polyadic Entropy, Synergy and Redundancy among Statistically Independent Processes in Nonlinear Statistical Physics with Microphysical Codependence

## Abstract

**:**

## 1. Introduction

#### 1.1. General Motivation

#### 1.2. Statistical and Information Entropy

#### 1.3. Information Redundancy

#### 1.4. Information Synergy

## 2. Polyadic “Non-Extensive” Entropies

#### 2.1. The Fundamentals

#### 2.2. Dyadic Systems

#### 2.3. Triadic Systems

## 3. Polyadic Synergy and Redundancy

#### 3.1. Synergy and Redundancy Emerging among Statistically Independent Variables

#### 3.2. Dyadic Form

#### 3.3. Triadic Form

## 4. Concluding Remarks

- Factorable probabilities do not necessarily lead to additive entropies.
- Microscale codependence does not necessarily lead to macroscale codependence.
- Macroscale independendence does not necessarily imply microscale independence.

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Perdigão, R.A.P. Polyadic Entropy, Synergy and Redundancy among Statistically Independent Processes in Nonlinear Statistical Physics with Microphysical Codependence. *Entropy* **2018**, *20*, 26.
https://doi.org/10.3390/e20010026

**AMA Style**

Perdigão RAP. Polyadic Entropy, Synergy and Redundancy among Statistically Independent Processes in Nonlinear Statistical Physics with Microphysical Codependence. *Entropy*. 2018; 20(1):26.
https://doi.org/10.3390/e20010026

**Chicago/Turabian Style**

Perdigão, Rui A. P. 2018. "Polyadic Entropy, Synergy and Redundancy among Statistically Independent Processes in Nonlinear Statistical Physics with Microphysical Codependence" *Entropy* 20, no. 1: 26.
https://doi.org/10.3390/e20010026