Dynamical transition in the TASEP with Langmuir kinetics: Mean-field theory

We develop a mean-field theory for the totally asymmetric simple exclusion process (TASEP) with open boundaries in order to investigate the so-called dynamical transition. The latter phenomenon appears as a singularity in the relaxation rate of the system toward its non-equilibrium steady state. In the high-density (low-density) phase, the relaxation rate becomes independent of the injection (extraction) rate at a certain critical value of the parameter itself, and this transition is not accompanied by any qualitative change in the steady-state behavior. We characterize the relaxation rate by means of bounds, becoming tight in the thermodynamic limit. These results are generalized to the TASEP with Langmuir kinetics, where particles can also bind to empty sites or unbind from occupied ones in the symmetric case of equal binding/unbinding rates. The theory predicts that a dynamical transition will occur in this case as well.