  The nature of coarse graining is intuitively "obvious", but it is rather
difficult to find explicit and calculable models of the coarse graining process
(and the resulting entropy flow) discussed in the literature. What we would
like to have at hand is some explicit and calculable process that takes an
arbitrary system, with specified initial entropy S, and monotonically and
controllably drives the entropy to its maximum value. This does not have to be
a physical process, in fact for some purposes it is better to deal with a
gedanken-process, since then it is more obvious how the "hidden information" is
hiding in the fine-grain correlations that one is simply agreeing not to look
at. We shall present several simple mathematically well-defined and easy to
work with conceptual models for coarse graining. We shall consider both the
classical Shannon and quantum von Neumann entropies, including models based on
quantum decoherence, and analyze the entropy flow in some detail. When
coarse-graining the quantum von Neumann entropy, we find it extremely useful to
introduce an adaptation of Hawking's super-scattering matrix. These explicit
models that we shall construct allow us to quantify and keep clear track of the
entropy that appears when coarse-graining the system, and the information that
can be hidden in unobserved correlations. (While not the focus of the current
article, in the longer run these considerations are of interest when addressing
black hole information puzzle.)
