  The dissipative dynamics of the spin chain coupled to the non-Markovian
magnonic reservoir was studied. The chirality of the chain is formed due to the
magnetoelectric coupling. We explored the sign of the trace distance derivative
and found the alternating positive/negative periods in system's time evolution.
The negative sign is associated with the flow of information from the system to
the bath and decrease in states distinguishability, while the positive sign is
related to the flow of the information in the opposite direction and increase
in distinguishability. We found the distinct effect of the applied electric and
magnetic fields. While the Dzyaloshinskii-Moriya interaction and external
electric field lead to reshuffling of the periods, the applied magnetic field
leads to the swift positive-negative transitions. Thus, in the helical quantum
rings coupled to the non-Markovian magnonic baths, it is possible to control
the directions of information flow through the external fields.
