  We show that the total kinetic energy (TKE) of nuclei after the spontaneous
fission of $^{258}$Fm can be well reproduced using simple assumptions on the
quantum collective phase-space explored by the nucleus after passing the
fission barrier. Assuming energy conservation and phase-space exploration
according to the stochastic mean-field approach, a set of initial densities is
generated. Each density is then evolved in time using the nuclear
time-dependent density-functional theory. This approach goes beyond mean-field
by allowing spontaneous symmetry breaking as well as a wider dynamical
phase-space exploration leading to larger fluctuations in collective space. The
total kinetic energy and mass distributions are calculated. New information on
the fission process: fluctuations in scission time, strong correlation between
TKE and collective deformation of daughter nuclei as well as pre- and
post-scission particle emission, are obtained.
