  We investigate steady states of macroscopic quantum systems under dissipation
not obeying the detailed balance condition. We argue that the Gibbs state at an
effective temperature gives a good description of the steady state provided
that the system Hamiltonian obeys the eigenstate thermalization hypothesis
(ETH) and the perturbation theory in the weak system-environment coupling is
valid in the thermodynamic limit. We derive a criterion to guarantee the
validity of the perturbation theory, which is satisfied in the thermodynamic
limit for sufficiently weak dissipation when the Liouvillian is gapped for
bulk-dissipated systems, while the perturbation theory breaks down in
boundary-dissipated chaotic systems due to the presence of diffusive
transports. We numerically confirm these theoretical predictions. This work
suggests a connection between steady states of macroscopic open quantum systems
and the ETH.
