  We investigate the steady state properties arising from the open system
dynamics described by a memoryless (Markovian) quantum collision model,
corresponding to a master equation in the ultra-strong coupling regime. By
carefully assessing the work cost of switching on and off the
system-environment interaction, we show that only a coupling Hamiltonian in the
energy-preserving form drives the system to thermal equilibrium, while any
other interaction leads to non-equilibrium steady states that are supported by
steady-state currents. These currents provide a neat exemplification of the
housekeeping work and heat. Furthermore, we characterize the specific form of
system-environment interaction that drives the system to a steady-state
exhibiting coherence in the energy eigenbasis, thus, giving rise to families of
states that are non-passive.
