  Path integrals have, over the years, proven to be an extremely versatile tool
for simulating the dynamics of open quantum systems. The initial limitations of
applicability of these methods in terms of the size of the system has steadily
been overcome through various developments, making numerical explorations of
large systems a more-or-less regular feature. However, these simulations
necessitate a detailed description of the system-environment interaction
through accurate spectral densities, which are often difficult to obtain.
Additionally, for several processes, such as spontaneous emission, one only has
access to a rough estimation of an empirical timescale, and it is not possible
to really define a proper spectral density at all. In this communication, an
approach of incorporating such processes within an exact path integral
description of other dissipative modes is developed through the
Nakajima-Zwanzig master equations. This method will allow for a numerically
exact non-perturbative inclusion of the degrees of freedom that are properly
described by a bath using path integrals, while incorporating the empirical
time scale through the Lindblad master equation. The cost of this approach is
dominated by the cost of the path integral method used, and the impact of the
Lindbladian terms is effectively obtained for free. This path integral Lindblad
dynamics method is demonstrated with the example of electronic excitation
transfer in a 4-site model of the Fenna-Matthews-Olson complex with the exciton
has a propensity of being "lost" to the charge transfer state at the third
chromophore. The impact of different time-scales of abstraction of the exciton
is illustrated at no extra cost.
