  The chain rule for the Shannon and von Neumann entropy, which relates the
total entropy of a system to the entropies of its parts, is of central
importance to information theory. Here we consider the chain rule for the more
general smooth min- and max-entropy, used in one-shot information theory. For
these entropy measures, the chain rule no longer holds as an equality, but
manifests itself as a set of inequalities that reduce to the chain rule for the
von Neumann entropy in the i.i.d. case.
