  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.
