  We analyze the long-time evolution of open quantum many-body systems using a
variational approach. For the dissipative Ising model, where mean-field theory
predicts a wide region of bistable behavior, we find genuine bistability only
at a singular point, confirming the previously suggested picture of a first
order transition. The situation is dramatically different when considering a
majority-voter model including three-body interactions, where we find bistable
behavior in an extended region, owing to the breaking of detailed balance in
the the effective description of the system. In this model, genuine bistability
persists even when quantum fluctuations are added.
