  We investigate the dynamics of information among the parties of tripartite
systems. We start by proving two results concerning the monogamy of mutual
information. The first one states that mutual information is monogamous for
generic tripartite pure states. The second shows that in general mutual
information is monogamous only if the amount of genuine tripartite correlations
is large enough. Then, we analyze the internal dynamics of tripartite systems
whose parties do not exchange energy. In particular, we allow for one of the
subsystems to play the role of a finite thermal bath. As a result, we find a
typical scenario in which local information tends to be converted into
delocalized information. Moreover, we show that (i) the information flow is
reversible for finite thermal baths at low temperatures, (ii) monogamy of
mutual information is respected throughout the dynamics, and (iii) genuine
tripartite correlations are typically present. Finally, we analytically
calculate a quantity capable of revealing favorable regimes for
non-Markovianity in our model.
