Application of the Stochastic Mode-reduction Strategy and a Priori Prediction of Symmetry Breaking in Stochastic Systems with Underlying Symmetry

We consider application of the stochastic mode-reduction strategy to a particular class of coupled models where a part of self-interactions of the slow variables is given by a rotationally invariant gradient system. The stochastic mode-reduction strategy is utilized to derive stochastic reduced models which yield a simple description of the phenomena resulting from breaking the original rotational symmetry. It is demonstrated that the direction of the symmetry breaking can be predicted a priori without any knowledge of the statistical behavior of the fast modes.