Stationary distributions for systems with competing creation-annihilation dynamics

The authors have developed a simple, systematic method to investigate the existence of stationary probability distributions (SPDs) for interacting particle (or spin) lattice systems exhibiting steady non-equilibrium states. The latter originate in a competition between several creation-annihilation (spin-flip) kinetic mechanisms, say each acting presuming a different bath temperature, particle (spin) interactions strength or chemical potential (magnetic field). It follows the existence of SPDs for a large class of these systems which may thus be studied by simply applying the techniques of equilibrium theory. The method is illustrated with several examples bearing a practical interest.