Multibalance conditions in nonequilibrium steady states

We study a new balance condition multibalance to obtain the nonequilibrium steady states of a class of nonequilibrium lattice models on a ring where a particle hops from a particular site to its nearest and next nearest neighbours. For the well-known zero range process (ZRP) with asymmetric hop rates, with this balance condition, we obtain the conditions on hop rates that lead to a factorized steady state (FSS). We show that this balance condition gives the cluster-factorized steady state (CFSS) for finite range process (FRP) and other models. We also discuss the application of multibalance condition to two species FRP model with hop rates ranging up to K nearest neighbours.