  Friction coefficients for the fusion reaction $^{16}$O+$^{16}$O $\rightarrow$
$^{32}$S are extracted based on both the time-dependent Hartree-Fock and the
time-dependent density matrix methods. The latter goes beyond the mean-field
approximation by taking into account the effect of two-body correlations, but
in practical simulations of fusion reactions we find that the total energy is
not conserved. We analyze this problem and propose a solution that allows for a
clear quantification of dissipative effects in the dynamics. Compared to
mean-field simulations, friction coefficients in the density-matrix approach
are enhanced by about $20 \, \%$. An energy-dependence of the dissipative
mechanism is also demonstrated, indicating that two-body collisions are more
efficient at generating friction at low incident energies.
