Non-equilibrium phase transition I have come across the term Non-equilibrium phase transition. And unfortunately I can't find any examples of such a phenomenon.
What examples of nonequilibrium phase transitions are known? Are there some analogies with "Ising-like" models, which clarify the main peculiarity of such transitions?  How to distinguish such a transition from equilibrium phase transitions?
 A: Good morning:
I came across the same question a while ago. Let me share some insights with you.
When referring to equilibrium based phase change, that would be having the species freely partitioning towards one single equilibrium stage. There, Gibbs Free Energy of the System is minimum (for constant P and T).
However, if one thinks of a membrane based separation, not all pathways are kinetically feasible. For example, in Reverse Osmosis, the solvent is the preferred species to pass through the holes (permeate). Not so is the case for solutes, that are "retained" (rentetate).
In both situations, the inlets are already in equilibrium. To reach another thermodynamic state (for example inflow, P and T), there is a need for an external action.
For equilibrium-based evaporation, one must add heat into the system (causing migration to the gas phase) or applying vacuum (lowering the bubble point of the liquid).
For Reverse Osmosis, one must apply mechanical force to overcome the osmotic pressure.  The system will react with selective permeation, migrating solvent to a purer stream.
In conclusion, the main difference is whether all species are kinetically free to evolve or not.
A: Non-equilibrium phase transitions may mean different things, depending on the context: it could refer to dynamical critical phenomena or to dissipative structures.
Dynamic critical phenomena are usual critical phenomena (aka equilibrium phase transitions) studied under non-equilibrium conditions. For example, one may consider behavior of an Ising farromagnet when a temperature is swept across critical point at a finite speed, or when the change of magnétisation is caused by varying magnetic field. One could also study response of a strongly correlated system beyond the linear response, as, e.g., non-equilibrium transport through superconducting islands.
Dissipative structures are symmetry breaking phenomena occurring in systems out of equilibrium. Unlike in the case of the dynamical critical phenomena, different phases may not exist when the system is in equilibrium, but appear only when there are non-zero fluxes of energy, matter, etc. flowing through the system. A classical example is Benard convection in a heated liquid. More important applications are explaining the origin and existence of life or the Earth's geochemistry. 
Theory of the dissipative structures, and indeed non-equilibrium thermodynamics, was pioneered and developed by Prigogine and his school. It however remains controversial - partially because some if its ideas are poorly understood/popularized by the broader community (e.g., the coexistence of minimum entropy production principle and maximum entropy production principle, see this post), but also because its applicability to key problems, such as the origin of life on Earth, has not been convincingly demonstrated - see the Anderson's critique.
Moreover, although studying of symmetry breaking in non-equilibrium conditions is certainly a part of physics, the problems of interest are often of interdisciplinary nature, and typically tackled by people with no special knowledge in in critical phenomena or even thermodynamics, and published in journals overlooked by the majority of physicists  (e.g., see here). On the other hand, the examples accessible to physicist of general background, such as Benard convection or Schlögl model, are too specific to be of broad interest and stimulate extensive theoretical efforts.
