A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analogue of such a theory. Specifically, we consider local dissipative dynamics preparing a steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive fluctuations in a local order parameter. We show that for all such processes satisfying detailed balance, there exist metastable symmetry-breaking states, i.e., states that become stationary in the thermodynamic limit and give a finite value to the order parameter. We give results both for discrete and continuous symmetries and explicitly show how to construct the symmetry-breaking states. Our results show in a simple way that, in large systems, local dissipative dynamics satisfying detailed balance cannot uniquely and efficiently prepare states with extensive fluctuations with respect to local operators. We discuss the implications of our results for quantum simulators and dissipative state preparation.One of the backbones of modern physics is the theory of phase transitions, whereby a phase transition is accompanied by a change of an order parameter reflecting the spontaneous breakdown of a symmetry [1]. Although this paradigm has been enriched by the existence of topological phases of matter, there still remains a lot to be learned about these more conventional types of phase transitions.Usually, phase transitions are studied from a kinematic point of view: While at high temperatures the Gibbs state is unique [2], below a critical temperature several thermal states, corresponding to the different symmetry-broken phases, exist in the thermodynamic limit. In systems of finite volume the thermal state at any finite temperature is always unique and order parameters associated with a symmetry of the Hamiltonian vanish due to the corresponding symmetry of the Gibbs state. Nevertheless, phase transitions can be associated with extensive fluctuations of the order parameter and can therefore already be witnessed in finite systems. More concretely, the value of order parameters in symmetry-breaking thermal states in the thermodynamic limit due to infinitesimal symmetry-breaking fields can be lower bounded by the magnitude of fluctuations in large but finite volumes without symmetry-breaking fields [3][4][5].Such kinematic results do not say anything about how the different phases of matter are prepared by a physical mechanism. In this work, we provide a dynamic picture: we consider the preparation of states with extensive fluctuations of a local order parameter in large volumes by dissipative opensystems dynamics, generated by local Liouvillians fulfilling detailed balance. We then show that under such conditions there are always symmetry-breaking sequences of metastable states, which converge to steady states in the thermodynamic limit. ...