  We apply in a schematic model a theory beyond mean-field, namely Stochastic
Time-Dependent Hartree-Fock (STDHF), which includes dynamical electron-electron
collisions on top of an incoherent ensemble of mean-field states by occasional
2-particle-2-hole ($2p2h$) jumps. The model considered here is inspired by a
Lipkin-Meshkov-Glick model of $\Omega$ particles distributed into two bands of
energy and coupled by a two-body interaction. Such a model can be exactly
solved (numerically though) for small $\Omega$. It therefore allows a direct
comparison of STDHF and the exact propagation. The systematic impact of the
model parameters as the density of states, the excitation energy and the
bandwidth is presented and discussed. The time evolution of the STDHF compares
fairly well with the exact entropy, as soon as the excitation energy is
sufficiently large to allow $2p2h$ transitions. Limitations concerning low
energy excitations and memory effects are also discussed.
