  One approach to deriving the kinetic equations relies upon work which generalizes ergodic theory. Relying upon the instability of trajectories, one tries to show that a region of phase points representing the possible micro-states for a system prepared in a non-equilibrium condition will, if the constraints are changed, eventually evolve into a set of phase points that is “coarsely” spread over the entire region of phase space allowed by the changed constraints. The old region cannot “finely” cover the new region by a fundamental theorem of dynamics (Liouville's theorem). But, in a manner first described by Gibbs, it can cover the region in a coarse-grained sense. To show that a collection of points will spread in such a way (in the infinite time limit at least) one tries to show the system possessed of an appropriate “randomization” property. In order of increasing strength such properties include weak-mixing, mixing, being a K system or being a Bernoulli system. Other, topological as opposed to measure-theoretic, approaches to this problem exist as well.