Taking a two-level system interacting with a two-band environment as an example, we discuss the non-Markovianity and initial system-environment correlations for the generalized Lindblad master equation by using a recently introduced measure given by Breuer et al. Our results show that the initial states of the environment and initial system-environment correlations have strong effects on the non-Markovianity of the reduced system. Moreover, we also show that information and energy can flow in different directions, i.e., energy flows to the system while information flows from the system, which is quite different from previous results.
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