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We solve a simple model that supports a dynamic phase transition and showconditions for the existence of the transition. Using methods of largedeviation theory we analytically compute the probability distribution foractivity and entropy production rates of the trajectories on a large ring witha single heterogeneous link. The corresponding joint rate function demonstratestwo dynamical phases - one localized and the other delocalized, but themarginal rate functions do not always exhibit the underlying transition.Symmetries in dynamic order parameters influence the observation of atransition, such that distributions for certain dynamic order parameters neednot reveal an underlying dynamical bistability. Solution of our model systemfurthermore yields the form of the effective Markov transition matrices thatgenerate dynamics in which the two dynamical phases are at coexistence. Wediscuss the implications of the transition for the response of bacterial cellsto antibiotic treatment, arguing that even simple models of a cell cyclelacking an explicit bistability in configuration space will exhibit abistability of dynamical phases.

Heterogeneity-induced large deviations in activity and (in some cases) entropy production