We investigate the link between information and thermodynamics embodied by Landauers principle in the open dynamics of a multipartite quantum system. Such irreversible dynamics is described in terms of a collisional model with a finite temperature reservoir. We demonstrate that Landauers principle holds, for such a configuration, in a form that involves the flow of heat dissipated into the environment and the rate of change of the entropy of the system. Quite remarkably, such a principle for {it heat and entropy power} can be explicitly linked to the rate of creation of correlations among the elements of the multipartite system and, in turn, the non-Markovian nature of their reduced evolution. Such features are illustrated in two exemplary cases.
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