  Under natural conditions, excitation of biological molecules, which display
non-unitary open system dynamics, occurs via incoherent processes such as
temperature changes or irradiation by sunlight/moonlight. The dynamics of such
processes is explored analytically in a non-Markovian generic model.
Specifically, a system S in equilibrium with a thermal bath TB is subjected to
an external incoherent perturbation BB (such as sunlight) or another thermal
bath TB', which induces time evolution in (S+TB). Particular focus is on (i)
the extent to which the resultant dynamics is coherent, and (ii) the role of
"stationary coherences", established in the (S+TB) equilibration, in the
response to the second incoherent perturbation. Results for systems with
parameters analogous to those in light harvesting molecules in photosynthesis
show that the resultant dynamical behaviour is incoherent beyond a very short
response to the turn-on of the perturbation.
