Dynamical aspects of spontaneous symmetry breaking in driven flow with exclusion

We present a numerical study of a two-lane version of the stochastic nonequilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally imposed particle injection (α) and ejection (β) rates, spontaneous symmetry breaking can occur. We investigate the statistics and internal structure of the stochastically induced transitions or "flips," which occur between opposite broken-symmetry states as the system evolves in time. From the distribution of time intervals separating successive flips, we show that the evolution of the associated characteristic times against externally imposed rates yields information regarding the proximity to a critical point in parameter space. On short timescales, we probe for the possible existence of precursor events to a flip between opposite broken-symmetry states. We study an adaptation of domain-wall theory to mimic the density reversal process associated with a flip.