The dynamics of a mixed quantum-classical system, in which the classical subsystem interacts witha dissipative bath, is investigated. This description of the dynamics will be appropriate if the detailsof the bath dynamics are unimportant but its presence plays an important role in the dissipation ofenergy to the environment. In this dynamical description, which can be simulated employing anensemble of stochastic surface-hopping trajectories, the strength of the dissipation is controlled bya friction coefficient. We show that if decoherence, whose effects are controlled by the bath friction,is sufficiently rapid, the equation of motion can be reduced to a master equation. Thus, decoherenceand the validity of master equation models may be explored as a function of bath friction. We usethis framework to study the mechanism of decoherence in a simple model nonadiabatic chemicalreaction.
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