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.
Highlights
With polyadic entropy functionals at hand, we are in position to quantify the synergy and redundancy associated to the nonlinear microphysical footprint onto the macrophysics, with special interest regarding the cross-variable microphysical interactions that develop once the once-separate variables come together forming the joint system polyad
The formulation of generalized entropy functionals where microphysical nonlinearities are taken into account is relevant for the evaluation of entropy functionals in systems the microphysics of which are nonlinearly codependent, e.g., for anomalous diffusion, nonlinear coevolution and mixing among heterogeneous yet interconnected media e.g., across a boundary permeable to momentum and/or heat transfer
A new measure of polyadic synergy has been introduced and discussed that takes into account the microphysical codependence through the entropic parameters present in generalized “non-extensive”
Summary
Traditional information-theoretical measures quantify the amount of macroscale information i.e., statistical properties required to characterize a system (Information Entropy, [1,2]), the amount of information shared i.e., redundant among processes (Redundant Information, e.g., the measures in [2,3]), and the amount of innovative information emerging from the non-redundant cooperation among processes (Synergistic Interaction Information, e.g., the measures in [4,5]). The information-theoretical measures of entropy, redundancy and synergy are traditionally formulated assuming independence among the microstates living within a macroscale variable of interest. The latter is assumed to represent a random process in which each observational event is an independent realization within a distribution embodying the statistical envelope aggregating the aforementioned microstates. While evaluating statistical relationships among macroscale variables, the microphysical interactions within at a statistical mechanical level remain elusive. If no such interactions take place e.g., in a perfect gas, the traditional information metrics will be accurate. Entropy 2018, 20, 26 holds, such as in complex systems with nonlocal interactions leading to long-range codependence and multifractal scaling characteristics
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