  We investigate the irreversible entropy production of a qubit in contact with
an environment modelled by a microscopic collision model both in Markovian and
non-Markovian regimes. Our main goal is to contribute to the discussions on the
relationship between non-Markovian dynamics and negative entropy production
rates. We employ two different types of collision models that do or do not keep
the correlations established between the system and the incoming environmental
particle, while both of them pertain to their non-Markovian nature through
information backflow from the environment to the system. We observe that as the
former model, where the correlations between the system and environment is
preserved, gives rise to negative entropy production rates in the transient
dynamics, the latter one always maintains positive rates, even though the
convergence to the steady-state value is slower as compared to the
corresponding Markovian dynamics. Our results suggest that the mechanism
underpinning the negative entropy production rates is not solely
non-Markovianity through information backflow, but rather the contribution to
it through established system-environment correlations.
