  The time-dependent fluorescence Stokes shifts monitors the relaxation of the
polarization of a polar solvent in the surroundings of a photoexcited solute
molecule, but also the structural variation of the solute following
photoexcitation and the subsequent molecular charge redistribution. Here, we
formulate a simple nonequilibrium quantum theory of solvation for an explicitly
time-dependent continuous solvent. The time-dependent solvent induces
nonequilibrium fluctuations on the solvent dynamics which are directly
reflected in different time components in the time-dependent Stokes shift. We
illustrate the structural dynamics in the presence of an explicitly
time-dependent solvent by the example of a dynamically shrinking solute which
leads to a bi-modal Stokes shift. Interestingly, both contributions are
mutually coupled. Furthermore, we can explain a prominent long-tail decay of
the Stokes shift associated to slow structural dynamical variations.
