Entropy Production in Open Systems: The Predominant Role of Intraenvironment Correlations

We show that the entropy production in small open systems coupled to environments made of extended baths is predominantly caused by the displacement of the environment from equilibrium rather than, as often assumed, the mutual information between the system and the environment. The latter contribution is strongly bounded from above by the Araki-Lieb inequality and therefore is not time extensive, in contrast to the entropy production itself. We confirm our results with exact numerical calculations of the system-environment dynamics.