  Focusing on the description of nontrivial properties of the energy transport
at quantum scale, we investigate asymmetrical quantum spin chains described by
boundary-driven $\mathit{XXZ}$ and $\mathit{XXX}$ Heisenberg models. We search
for symmetries properties of the Lindblad master equation related to the
dynamics of the system in order to establish properties of the steady state.
Under rather general assumptions for the target polarization at the boundaries,
we show the occurrence of an effect related to (but stronger than) energy
rectification, namely, the one-way street phenomenon, which is the existence of
an unique way for the energy flow. Precisely, the energy current does not
change in magnitude and direction as we invert the baths at the boundaries: its
direction is completely determined by the asymmetry in the bulk of the chain.
The results follow independent of the system size and of the transport regime.
Our findings show the ubiquitous occurrence of the one-way street phenomenon
for the energy flow in boundary-driven spin systems and, we believe, they shall
be an useful contribution to the area devoted to the investigation and building
of efficient quantum devices used to control and manipulate the energy current.
