Driven steady states: rules for transition rates

It is well known that transition rates in a canonical ensemble should respect the principle of detailed balance. What are the equivalent constraints that apply in non-equilibrium steady states, implied by maximization of information-entropy? The exact theorem for the non-equilibrium rates yields a substantial amount of non-trivial physics, illustrated in some examples including new results for a simple stochastic hopping model. Some of the implications for shear-controlled phase transitions are discussed.