  The reduced dynamics formalism has recently emerged as a powerful tool to
study the dynamics of non-equilibrium quantum impurity models in strongly
correlated regimes. Examples include the non-equilibrium Anderson impurity
model near the Kondo crossover temperature and the non-equilibrium Holstein
model, for which the formalism provides an accurate description of the reduced
density matrix of the system for a wide range of timescales. In this work, we
generalize the formalism to allow for non-system observables such as the
current between the impurity and leads. We show that the equation of motion for
the reduced observable of interest can be closed with the equation of motion
for the reduced density matrix and demonstrate the new formalism for a generic
resonant level model.
