Generalized kinetic theory of coarse-grained systems. II. Comparison of various approximations and coarse-grainings

In the first part of this article, recently published, the general kinetic theory of coarse-grained systems has been presented in the abstract formalism of communication theory developed by Shannon, Khinchin, Kolmogorov and other authors. In the second part of the article, presented below, we compare various approximations of this theory, and several kinds of coarse-grainings, focusing on their asymptotics. In particular, we introduce extensions of classical ergodic theorems and derive some rigorous results which allow for such comparison, although explicit calculations may be problematic.