Chain Rules for Smooth Min- and Max-Entropies
  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. 
Alexander Vitanov, Frederic Dupuis, Marco Tomamichel, Renato Renner
quant-ph math-ph math.MP