  We solve a simple model that supports a dynamic phase transition and show
conditions for the existence of the transition. Using methods of large
deviation theory we analytically compute the probability distribution for
activity and entropy production rates of the trajectories on a large ring with
a single heterogeneous link. The corresponding joint rate function demonstrates
two dynamical phases - one localized and the other delocalized, but the
marginal rate functions do not always exhibit the underlying transition.
Symmetries in dynamic order parameters influence the observation of a
transition, such that distributions for certain dynamic order parameters need
not reveal an underlying dynamical bistability. Solution of our model system
furthermore yields the form of the effective Markov transition matrices that
generate dynamics in which the two dynamical phases are at coexistence. We
discuss the implications of the transition for the response of bacterial cells
to antibiotic treatment, arguing that even simple models of a cell cycle
lacking an explicit bistability in configuration space will exhibit a
bistability of dynamical phases.
