  We consider two qubits interacting with a common bosonic bath, but not
directly between themselves. We derive the (bipartite) entanglement generation
conditions for Gaussian non-Markovian dynamical maps and show that they are
similar as in the Markovian regime; however, they depend on different physical
coefficients and hold on different time scales. Indeed, for small times, in the
non-Markovian regime entanglement is possibly generated on a shorter time scale
($\propto t^2$) than in the Markovian one ($\propto t$). Moreover, although the
singular coupling limit of non-Markovian dynamics yields Markovian ones, we
show that the same limit does not lead from non-Markovian entanglement
generation conditions to Markovian ones. Also, the entanglement generation
conditions do not depend on the initial time for non-Markovian open dynamics
resulting from couplings to bosonic Gaussian baths, while they may depend on
time for open dynamics originated by couplings to classical, stochastic
Gaussian environments.
