  In this work, we derived a transport equation based on a generalized equation
of time-dependent generator coordinate method (TDGCM) under the Gaussian
overlap approximation (GOA). The transport equation is obtained by using
quantum-mechanics phase space distributions under a ``quasi-particle" picture
and strategy of Bogoliubov-Born-Green-Kirkood-Yvon (BBGKY) hierarchy. The
theoretical advantage of this transport equation is that time evolution of
$s$-body phase space density distribution is coupled with $s+1$-body phase
space density distributions, and thus, non-adiabatic effects and dynamical
fluctuations could be involved by more collective degrees and entanglement of
phase space trajectories. In future, we will perform the numerical calculations
for fission nuclei after obtaining collective inertia and potential energy
surface (PES).
