  An equation describing the irreversible evolution of the local density of a
continuous medium without involving any statistical hypotheses and assumptions
is derived. The derivation is based on the smoothing of the microscopic dynamic
characteristics of a many-body system, taking into account the retardation of
the interactions between them. The resulting equation generalizes the classical
equation of motion for fluids. Several particular cases of the resulting
equation, as well as its connection with the dynamic density functional theory,
are considered.
