  Entropy production provides a general way to state the second law of
thermodynamics for non-equilibrium scenarios. In open quantum system dynamics,
it also serves as a useful quantifier of the degree of irreversibility. In this
work we shed light on the relation between correlations, initial preparation of
the system and non-Markovianity by studying a system of two harmonic
oscillators independently interacting with their local baths. Their dynamics,
described by a time-local master equation, is solved to show - both numerically
and analytically - that the global purity of the initial state of the system
influences the behaviour of the entropy production rate and that the latter
depends algebraically on the entanglement that characterise the initial state.
