  Consider local dephasing processes of a qubit that interacts with a
structured reservoir of frequency modes or a thermal bath, with Ohmic-like
spectral density (SD). It is known that non-Markovian evolution appears
uniquely above a temperature-dependent critical value of the Ohmicity
parameter, and non-Markovianity can be induced by properly engineering the
external environment. In the same scenario, we find that the flow of quantum
information shows regular patterns: alternate directions appear in
correspondence of periodical intervals of the Ohmicity parameter $\alpha_0$.
The information flows back into the system over long times for
$2+4n<\alpha_0<4+4n$, at zero temperature, and for $3+4n<\alpha_0<5+4n$, at
non-vanishing temperatures, where $n=0,1,2,\ldots$. Otherwise, the long time
information flows into the environment. In the transition from vanishing to
arbitrary non-vanishing temperature, the long time back-flow of information is
stable for $3+4n<\alpha_0<4+4n$, while it is reverted for $2+4n<\alpha_0<3+4n$
and $4+4n<\alpha_0<5+4n$. The patterns of the information flow are not altered
if the low frequency Ohmic-like profiles of the SDs are perturbed with
additional factors that consist in arbitrary powers of logarithmic forms.
Consequently, the flow of information can be controlled, directed and reverted
over long times by engineering a wide variety of reservoirs that includes and
continuously departs from the Ohmic-like structure at low frequencies.
Non-Markovianity and recoherence appear according to the same rules along with
the back-flow of information.
