Dynamical Widom-Rowlinson model and its mesoscopic limit

We consider the non-equilibrium dynamics for the Widom-Rowlinson model (without hard-core) in the continuum. The Lebowitz-Penrose-type scaling of the dynamics is studied and the system of the corresponding kinetic equations is derived. In the space-homogeneous case, the equilibrium points of this system are described. Their structure corresponds to the dynamical phase transition in the model. The bifurcation of the system is shown.