  Quantum non-Markovianity is crucially related to the study of dynamical maps,
which are usually derived for initially factorized system-bath states. We here
demonstrate that linear response theory also provides a way to derive dynamical
maps, but for initially correlated (and in general entangled) states.
Importantly, these maps are always time-translational invariant and allow for a
much simpler quantification of non-Markovianity compared to previous
approaches. We apply our theory to the Caldeira-Leggett model, for which our
quantifier is valid beyond linear response and can be expressed analytically.
We find that a classical Brownian particle coupled to an Ohmic bath can already
exhibit non-Markovian behaviour, a phenomenon related to the initial state
preparation procedure. Furthermore, for a peaked spectral density we
demonstrate that there is no monotonic relation between our quantifier and the
system-bath coupling strength, the sharpness of the peak or the resonance
frequency in the bath.
