  This work provides a detailed derivation of a generalized quantum
Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical
processes. The path integral method pioneered by Caldeira and Leggett (CL)
[Caldeira and Leggett, Physica A 121, 587 (1983)] is extended for a
nonequilibrium influence functional, which has been obtained for general cases
where the ground and the excited electronic state baths can be different. Both
nonequilibrium and non-Markovian effects are accounted for consistently by
expanding the paths in the exponents of the influence functional with respect
to time up to the second order. This procedure results in approximations
involving only single time integrations for the exponents of the influence
functional but with additional time dependent boundary terms that have been
ignored in previous works. The boundary terms complicate the derivation of a
time evolution equation, but do not affect position dependent physical
observables or the dynamics in the steady state limit. For an effective density
operator with the boundary terms factored out, a time evolution equation is
derived through short time expansion of the effective action followed by
Gaussian integrations in analytically continued complex domain of space. This
leads to a compact form of GQFPE with time dependent kernels and additional
terms, which make the resulting equation the Dekker form [H. Dekker, Phys. Rep.
80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic
spectral density with Drude cutoff, which shows that the new GQFPE satisfies
the positive definiteness condition in medium to high temperature limit.
