Steady-state thermodynamics: reservoir independence

For stochastic lattice models in spatially uniform nonequilibrium steady states, a thermodynamic temperature T and chemical potential μ can be defined via coexistence with heat and particle reservoirs. Here we ask whether the values so obtained depend on the nature of the exchange between system and reservoir. For example, a stochastic particle reservoir is usually taken to insert or remove a single particle in each exchange, but one may also consider a reservoir that inserts or removes a pair of particles in each event. In equilibrium, equivalence of pair and single-particle reservoirs is guaranteed by the canonical form of the probability distribution on configuration space. We examine whether this equivalence persists in nonequilibrium steady states.