Abstract
This paper carries out a cluster mean-field analysis for spontaneous symmetric breaking in a two-lane asymmetric exclusion process with narrow entrances and parallel update. We demonstrate that the asymmetric low-density/low-density phase does not exist, based on a current minimization principle. With the increase of the cluster number in the cluster mean-field analysis, an exponential decay of the boundary between asymmetric high-density/low-density phase and symmetric low-density phase as well as the bulk density in the symmetric low-density phase has been observed, which enables us to predict the phase boundary and the bulk density in the exact solution. The predicted results are in agreement with simulations.
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