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The information shared among observables representing processes of interestis traditionally evaluated in terms of macroscale measures characterizingaggregate properties of the underlying processes and their interactions.Traditional information measures are grounded on the assumption that theobservable represents a memoryless process without any interaction amongmicrostates. Generalized entropy measures have been formulated in non-extensivestatistical mechanics aiming to take microphysical codependence into account inentropy quantification. By taking them into consideration when formulatinginformation measures, the question is raised on whether and if so how muchinformation permeates across scales to impact on the macroscale informationmeasures. The present study investigates and quantifies the emergence ofmacroscale information from microscale codependence among microphysics. Inorder to isolate the information emergence coming solely from the nonlinearlyinteracting microphysics, redundancy and synergy are evaluated among macroscalevariables that are statistically independent from each other but notnecessarily so within their own microphysics. Synergistic and redundantinformation are found when microphysical interactions take place, even if thestatistical distributions are factorable. These findings stress the added valueof nonlinear statistical physics to information theory in coevolutionarysystems.

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