Abstract:
Motivated by the wide occurrence of limited resources in many real-life systems, we investigate two-lane totally
asymmetric simple exclusion process with constrained entrances under finite supply of particles. We analyze
the system within the framework of mean-field theory and examine various complex phenomena, including
phase separation, phase transition, and symmetry breaking. Based on the theoretical analysis, we analytically
derive the phase boundaries for various symmetric as well as asymmetric phases. It has been observed that the
symmetry-breaking phenomenon initiates even for very small number of particles in the system. The phases
with broken symmetry originates as shock-low density phase under limited resources, which is in contrast to the
scenario with infinite number of particles. As expected, the symmetry breaking continues to persist even for higher
values of system particles. Seven stationary phases are observed, with three of them exhibiting symmetry-breaking
phenomena. The critical values of a total number of system particles, beyond which various symmetrical and
asymmetrical phases appear and disappear are identified. Theoretical outcomes are supported by extensive Monte
Carlo simulations. Finally, the size-scaling effect and symmetry-breaking phenomenon on the simulation results
have also been examined based on particle density histograms.
