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Friction coefficients for the fusion reaction $^{16}$O+$^{16}$O $\rightarrow$$^{32}$S are extracted based on both the time-dependent Hartree-Fock and thetime-dependent density matrix methods. The latter goes beyond the mean-fieldapproximation by taking into account the effect of two-body correlations, butin practical simulations of fusion reactions we find that the total energy isnot conserved. We analyze this problem and propose a solution that allows for aclear quantification of dissipative effects in the dynamics. Compared tomean-field simulations, friction coefficients in the density-matrix approachare enhanced by about $20 \, \%$. An energy-dependence of the dissipativemechanism is also demonstrated, indicating that two-body collisions are moreefficient at generating friction at low incident energies.

Two-body dissipation effect in nuclear fusion reactions