What's the reasoning behind calling it non-equilibrium matter? Sure if you need to keep sending in laser pulses you can't exactly call it an equilibrium, but the original definition had periodic behaviour in the ground-state, which you'd think would be considered an an equilibrium.
It's not a thermodynamic equilibrium. The system does not have maximum entropy, and so, eventually the spin crystal will decay. The problem is eventually might be larger than the age of the universe by a factor of some really really large number
