  Ever since the insight spreaded that tailored dissipation can be employed to
control quantum systems and drive them towards pure states, the field of
non-equilibrium quantum mechanics gained remarkable momentum. So far research
focussed on emergent phenomena caused by the interplay and competition of
unitary Hamiltonian and dissipative Markovian dynamics. In this manuscript we
zero in on a so far rather understudied aspect of open quantum systems and
non-equilibrium physics, namely the utilization of purely dissipative couplings
to explore pure quantum phases and non-equilibrium phase transitions. To
illustrate this concept, we introduce and scrutinize purely dissipative
counterparts of (1) the paradigmatic transverse field Ising model and (2) the
considerably more complex $\mathbb{Z}_2$ lattice gauge theory with coupled
matter field. We show that, in mean field approximation, the non-equilibrium
phase diagrams parallel the (thermal) phase diagrams of the Hamiltonian "blue
print" theories qualitatively.
