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Entropy 2018, 20(1), 26; https://doi.org/10.3390/e20010026

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

Institute of Hydraulic Engineering, Technische Universität Wien (TU Wien), Karlsplatz 13/222, 1040 Vienna, Austria
Received: 5 December 2017 / Revised: 26 December 2017 / Accepted: 3 January 2018 / Published: 4 January 2018
(This article belongs to the Special Issue Theoretical Aspect of Nonlinear Statistical Physics)
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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. View Full-Text
Keywords: polyadic entropy; synergy; redundancy; coevolution; non-extensive; nonlinear statistical physics; information theory polyadic entropy; synergy; redundancy; coevolution; non-extensive; nonlinear statistical physics; information theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Perdigão, R.A.P. Polyadic Entropy, Synergy and Redundancy among Statistically Independent Processes in Nonlinear Statistical Physics with Microphysical Codependence. Entropy 2018, 20, 26.

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