Exact integrable spin chains and transfer matrices related to models with stochastic dynamics

We present a general family of one-dimensional quantum Hamiltonians and two-dimensional transfer matrices that are exact integrable through the Bethe ansatz and describe the time fluctuations of classical one-dimensional stochastic models. These quantum chains are higher spin generalizations of the standard XXZ chain and the related stochastic models describe the asymmetric diffusion of particles where the particles have arbitrary sizes and belong to distinct classes with hierarchical order. The transfer matrices we present are connected with new 10-vertex models that generalizes the standard six vertex model. These transfer matrices describe the dynamics of of some stochastic cellular automata.