Cluster mean-field analysis for spontaneous symmetric breaking in a bidirectional two-lane system with narrow entrances and parallel update

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.

Existence of spontaneous symmetry breaking in two-lane totally asymmetric simple exclusion processes with an intersection*

“…Those theoretical analyses all indicated that the asymmetric phase does not exist. [22,23] However, the mechanism of the occurrence of SSB is still not well understood. [15] Yuan et al [18] investigated another two-lane TASEP.…”

Totally asymmetric simple exclusion processes on two intersected lanes

“…It means that the density of the upstream of the intersection site of the northbound lane is larger than that of the eastbound lane, i.e., ρ 2 − ρ 1 > 0. The flow rate of the downstream of the intersection site of the northbound lane is smaller than that of the eastbound lane, i.e., J 4 − J 3 < 0 [37,38]. Therefore, the asymmetric phase exists when 0 < β < β c , see fig.…”