Abstract
A collective, non-hamiltonian model for the dynamics of a classicalN-particle system is given. The Liouville statistics yields a hierarchy for the reduced distribution functions and the model has been chosen in such a way that the first of the hierarchy equations is the Vlasov equation regardless of collisions or correlations. The Gibbs entropy of such a system is not conserved albeit the one particle distribution function is a solution of the reversible Vlasov equation.