  In this paper we consider a bipartite system composed of two subsystems each
coupled to its own thermal environment. Based on a collision model, we mainly
study whether the approximation (i.e., the inter-system interaction is ignored
when modeling the system-environment coupling) is valid or not. We also address
the problem of heat transport unitedly for both conventional energy-preserving
system-environment interactions and non-energy preserving system-environment
interactions. For the former interaction, as the inter-system interaction
strength increases, at first this approximation gets worse as expected, but
then counterintuitively gets better even for a stronger inter-system coupling.
For the latter interaction with asymmetry, this approximation gets
progressively worse. In this case we realize a perfect thermal rectification,
and we can not find apparent rectification effect for the former interaction.
Finally and more importantly, our results show that whether this approximation
is valid or not is closely related to the quantum correlations between the
subsystems, i.e., the weaker the quantum correlations, the more justified the
approximation and vice versa.
