  We explore signatures of the non-Markovianity in the time-resolved energy
transfer processes for quantum open systems. Focusing on typical systems such
as the exact solvable damped Jaynes-Cummings model and the general spin-boson
model, we establish quantitative links between the time-resolved energy current
and the symmetric logarithmic derivative quantum Fisher information (SLD-QFI)
flow, one of measures quantifying the non-Markovianity, within the framework of
non-Markovian master equations in time-local forms. From the relationships, we
find in the damped Jaynes-Cummings model that the SLD-QFI backflow from the
reservoir to the system always correlates with an energy backflow, thus we can
directly witness the non-Markovianity from the dynamics of the energy current.
In the spin-boson model, the relation is built on the rotating-wave
approximation, calibrated against exact numerical results, and proven reliable
in the weak coupling regime. We demonstrate that whether the non-Markovianity
guarantees the occurrence of an energy backflow depends on the bath spectral
function. For the Ohmic and sub-Ohmic cases, we show that no energy backflow
occurs and the energy current always flow out of the system even in the
non-Markovian regime. While in the super-Ohmic case, we observe that the
non-Markovian dynamics can induce an energy backflow.
