Abstract We study the flow of matter, momentum and energy in low-energy heavy-ion collisions. This is done by using the Wigner phase space distribution function to calculate quantum mechanical analogs of the classical distributions of the observables. We apply the Wigner transformation to time-dependent Hartree-Fock calculations of 16O+ 16O and 40Ca+ 40Ca reactions. Both static and dynamic features of the distribution functions are demonstrated. We find a significant energy flow perpendicular to the beam direction. The one-way matter current obtained from time-dependent Hartree-Fock calculations is reproduced well by a combination of two simplified models for the relative motion and tunneling.