  We prove strong existence and uniqueness for a reflection process $X$ in a
smooth, bounded domain $D$ that behaves like
obliquely-reflected-Brownian-motion, except that the direction of reflection
depends on a (spin) parameter $S$, which only changes when $X$ is on the
boundary of $D$ according to a physical rule. The process $(X,S)$ is a
degenerate diffusion.
  We show uniqueness of the stationary distribution by using techniques based
on excursions of $X$ from $\partial D$, and an associated exit system. We also
show that the process admits a submartingale formulation and use related
results to show examples of the stationary distribution.
