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We consider the one-dimensional driven ABC model under particle-conservingand particle-non-conserving processes. Two limiting cases are studied: (a) therates of the non-conserving processes are vanishingly slow compared with theconserving processes in the thermodynamic limit and (b) the two rates arecomparable. For case (a) we provide a detailed analysis of the phase diagramand the large deviations function of the overall density, G(r). The phasediagram of the non-conserving model, derived from G(r), is found to bedifferent from the conserving one. This difference, which stems from thenon-convexity of G(r), is analogous to ensemble inequivalence found inequilibrium systems with long-range interactions. An outline of the analysis ofcase (a) was given in an earlier letter. For case (b) we show that unlike theconserving model, the non-conserving model exhibits a moving density profile inthe steady-state with a velocity that remains finite in the thermodynamiclimit. Moreover, in contrast with case (a), the critical lines of theconserving and non-conserving models do not coincide. These are new featureswhich are present only when the rates of the conserving and non-conservingprocesses are comparable. In addition, we analyze G(r) in case (b) usingmacroscopic fluctuations theory. Much of the derivation presented in this paperis applicable to any driven-diffusive system coupled to an externalparticle-bath via a slow dynamics.

Non-equilibrium ensemble inequivalence and density large deviations in the ABC model