A remark on the choice of stochastic transition rates in driven nonequilibrium systems

We study nonequilibrium steady states of the driven lattice gas with two particles, using the most general stochastic transition rules that satisfy the local detailed balance condition. We observe that i) the universal $1/r^d$ long range correlation may be found already in the two-particle models, but ii) the magnitude (or even the existence/absence) of the long range correlation depends crucially on the rule for transition rates. The latter is in stark contrast with equilibrium dynamics, where all rules give essentially the same results provided that the detailed balance condition is satisfied.