  In a previous study we developed a mean-field theory of dynamical transitions
for the totally-asymmetric simple-exclusion process (TASEP) with open
boundaries and Langmuir kinetics, in the so-called balanced regime,
characterized by equal binding and unbinding rates. Here we show that simply
including the possibility of unbalanced rates gives rise to an unexpectedly
richer dynamical phase diagram. In particular, the current work predicts an
unusual type of dynamical transition, which exhibits certain similarities with
first-order phase transitions of equilibrium systems. We also point out that
different types of dynamical transition are accompanied by different structural
changes in the (mean-field) relaxation spectrum.
