  Einstein-Podolsky-Rosen steering describes a quantum correlation in addition
to entanglement and Bell nonlocality. However, conceptually different from
entanglement and Bell nonlocality, quantum steering has an asymmetric
definition. Motivated by the asymmetric definition of quantum steering, we
study the steerability of two-interacting qubits, which have asymmetric energy
levels, coupled with asymmetric environments. The asymmetric (nonequilibrium)
environments are two environments with different temperatures or chemical
potentials. The Bloch-Redfield equation is applied to study the dynamics of two
qubits and its long-time behavior. In our study, the steady-state steerability
is determined by an experimentally friendly steering criteria, which
demonstrates steering through the entanglement detection. Our results show that
the steady states of two asymmetric qubits have the advantage for one direction
of steering, compared to the symmetric setup. We also provide analytical
results on the minimal coupling strength between the two qubits in order to be
steerable. The asymmetric steerability is collectively determined by the nature
of the two qubits and the influence from equilibrium or nonequilibrium
environments. Nonequilibrium environments with the cost of nonzero entropy
production can enhance the steerability in one direction. We also show the
strict hierarchy of entanglement, steering and Bell nonlocality of the
nonequilibrium steady states, which shows a richer structure of steering than
entanglement and Bell nonlocality.
