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

TL;DR

This paper explores how microphysical interactions influence macroscale information measures in nonlinear statistical physics, revealing that synergy and redundancy emerge even among macroscale variables that are statistically independent but microphysically interconnected.

Contribution

It introduces a framework to quantify information emergence from microphysical codependence, highlighting the role of nonlinear interactions in information theory.

Findings

Synergistic and redundant information arise from microphysics interactions.

Macroscale variables can be independent statistically but still exhibit information sharing.

Nonlinear statistical physics enhances understanding of information flow in coevolutionary systems.

Abstract

The information shared among observables representing processes of interest is traditionally evaluated in terms of macroscale measures characterizing aggregate properties of the underlying processes and their interactions. Traditional information measures are grounded on the assumption that the observable represents a memoryless process without any interaction among microstates. Generalized entropy measures have been formulated in non-extensive statistical mechanics aiming to take microphysical codependence into account in entropy quantification. By taking them into consideration when formulating information measures, the question is raised on whether and if so how much information permeates across scales to impact on the macroscale information measures. The present study investigates and quantifies the emergence of macroscale information from microscale codependence among microphysics. In order to isolate the information emergence coming solely from the nonlinearly interacting microphysics, redundancy and synergy are evaluated among macroscale variables that are statistically independent from each other but not necessarily so within their own microphysics. Synergistic and redundant information are found when microphysical interactions take place, even if the statistical distributions are factorable. These findings stress the added value of nonlinear statistical physics to information theory in coevolutionary systems.