  We examine non-Markovian effects in an open quantum system from the point of
view of information flow. To this end, we consider the spin-boson model with a
cold reservoir, accounting for the exact time-dependent correlations between
the system and the bath to study the exchange of information and heat. We use
an information theoretic measure of the relevant memory effects and demonstrate
that the information backflow from the reservoir to the system does not
necessarily correlate with the backflow of heat. We also examine the influence
of temperature and coupling strength on the loss and gain of information
between the system and the bath. Finally, we discuss how additional driving
changes the backflow of information, giving rise to potential applications in
reservoir engineering.
