  We consider the microscopic solutions of the Boltzmann-Enskog equation
discovered by Bogolyubov. The fact that the time-irreversible kinetic equation
has time-reversible microscopic solutions is rather surprising. We analyze this
paradox and show that the reversibility or irreversibility property of the
Boltzmann-Enskog equation depends on the considered class of solutions. If the
considered solutions have the form of sums of delta-functions, then the
equation is reversible. If the considered solutions belong to the class of
continuously differentiable functions, then the equation is irreversible. Also,
we construct the so called approximate microscopic solutions. These solutions
are continuously differentiable and they are reversible on bounded time
intervals. This analysis suggests a way to reconcile the time-irreversible
kinetic equations with the time-reversible particle dynamics. Usually one tries
to derive the kinetic equations from the particle dynamics. On the contrary, we
postulate the Boltzmann-Enskog equation or another kinetic equation and treat
their microscopic solutions as the particle dynamics. So, instead of the
derivation of the kinetic equations from the microdynamics we suggest a kind of
derivation of the microdynamics from the kinetic equations.
