  We study the relationship between (non-)Markovian evolutions, established
correlations, and the entropy production rate. We consider a system qubit in
contact with a thermal bath and in addition the system is strongly coupled to
an ancillary qubit. We examine the steady state properties finding that the
coupling leads to effective temperatures emerging in the composite system, and
show that this is related to the creation of correlations between the qubits.
By establishing the conditions under which the system reaches thermal
equilibrium with the bath despite undergoing a non-Markovian evolution, we
examine the entropy production rate, showing that its transient negativity is a
sufficient sign of non-Markovianity.
