Ensemble reservoir equivalence in driven lattice gases

For stochastic lattice models in spatially uniform nonequilibrium steady states (NESS), temperature and chemical potential can be defined via coexistence with heat and particle reservoirs. We consider NESS in the driven lattice gas with nearest-neighbor exclusion. In weak contact with a particle reservoir, it attains a NESS with a fluctuating particle number, analogous to the grand canonical ensemble in equilibrium. Are the properties of this NESS equivalent to those found with fixed particle number? We report numerical evidence for such an ensemble equivalence between NESS in the limit of large system sizes. Additionally, we ask if the macroscopic properties depend on the nature of the exchange between system and reservoir. For example, although the stochastic interaction between system and reservoir usually involves exchange of a single particle, one may also consider a reservoir that inserts or removes pairs of particles. In equilibrium, equivalence of pair and single-particle reservoirs is guaranteed by the canonical form of the probability distribution on configuration space. We find that out of equilibrium, this equivalence no longer holds.