  One of the fundamental issues in the field of open quantum systems is the
classification and quantification of non-Markovianity. In the contest of
quantity-based measures of non-Markovianity, the intuition of non-Markovianity
in terms of information backflow is widely discussed. However, it is not easy
to characterize the information flux for a given system state and show its
connection to non-Markovianity. Here, by using the concepts from thermodynamics
and information theory, we discuss a potential definition of information flux
of an open quantum system, valid for static environments. We present a simple
protocol to show how a system attempts to share information with its
environment and how it builds up system-environment correlations. We also show
that the information returned from the correlations characterizes the
non-Markovianity and a hierarchy of indivisibility of the system dynamics.
