Entropy, Stochastic Matrices, and Quantum Operations
  The goal of the present paper is to derive some conditions on saturation of (strong) subadditivity inequality for the stochastic matrices. The notion of relative entropy of stochastic matrices is introduced by mimicking quantum relative entropy. Some properties of this concept are listed and the connection between the entropy of the stochastic quantum operations and that of stochastic matrices are discussed. 
Lin Zhang
quant-ph