On the existence of kinetic equations

The existence of the Boltzmann equation and its generalizations is studied by analysing the order of magnitude of their terms. As a consequence we conclude that the reduced distribution functions are not analytic in the density.

Irreversibility of the transport equations

On the generalization of the Boltzmann equation

Starting from the Liouville equation and making use of projection operator techniques we obtain a compact equation for the rate of change of then-particle momentum distribution function to any order in the density. This equation is exact in the thermodynamic limit. The terms up to second order in the density are studied and expressions are given for the errors committed when one makes the usual hypothesis to derive generalized Boltzmann equations. Finally the Choh-Uhlenbeck operator is obtained under additional assumptions.