Around Shannon's Interpretation for Entropy-preserving Stochastic   Averages
  We give various characterizations for a positive unital Tr-preserving map on a matrix algebra to preserve the von Neumann entropy of a state. Among others, it is given by that the map behaves as a *-automorphism. This is also equivalent to that the entropy of the stochastic matrix arising from the map and the state is zero. 
Marie Choda
math.OA