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We construct a one-dimensional totally asymmetric simple exclusion process(TASEP) on a ring with two segments having unequal hopping rates, coupled toparticle non-conserving Langmuir kinetics (LK) characterized by equalattachment and detachment rates. In the steady state, in the limit of competingLK and TASEP, the model is always found in states of phase coexistence. Weuncover a nonequilibrium phase transition between a three-phase and a two-phasecoexistence in the faster segment, controlled by the underlying inhomogeneityconfigurations and LK. The model is always found to be half-filled on averagein the steady state, regardless of the hopping rates and theattachment/detachment rate.

Phase coexistences and particle non-conservation in a closed asymmetric exclusion process with inhomogeneities