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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 coupling is ignored when modeling the system-environment interaction) is valid or not. We also address the problem of heat transport unitedly for both excitation-conserving system-environment interactions and non-excitation-conserving system-environment interactions. For the former interaction, as the inter-system interaction strength increases, at f
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