Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries

We consider a driven diffusive system with two types of particles, A and B, coupled at the ends to reservoirs with fixed particle densities. To define stochastic dynamics that correspond to boundary reservoirs we introduce projection measures. The stationary state is shown to be approached dynamically through an infinite reflection of shocks from the boundaries. We argue that spontaneous symmetry breaking observed in similar systems is due to placing effective impurities at the boundaries and therefore does not occur in our system. Monte-Carlo simulations confirm our results.