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One of the fundamental issues in the field of open quantum systems is theclassification and quantification of non-Markovianity. In the contest ofquantity-based measures of non-Markovianity, the intuition of non-Markovianityin terms of information backflow is widely discussed. However, it is not easyto characterize the information flux for a given system state and show itsconnection to non-Markovianity. Here, by using the concepts from thermodynamicsand information theory, we discuss a potential definition of information fluxof an open quantum system, valid for static environments. We present a simpleprotocol to show how a system attempts to share information with itsenvironment and how it builds up system-environment correlations. We also showthat the information returned from the correlations characterizes thenon-Markovianity and a hierarchy of indivisibility of the system dynamics.

Thermodynamic description of non-Markovian information flux of nonequilibrium open quantum systems