Stochastic quantum process
  I propose to treat quantum evolution as a stochastic process consisting from a sequence of doubly stochastic matrices, which naturally arise in the generalized quantum evolution. Then it is proved that the law of non-decreasing entropy is fulfilled and that the law characterizes doubly stochastic matrices. Finally, an application of the model to support the generalized second law of black hole thermodynamics and a relation to the quantum histories formulation of quantum physics appear. 
Jerzy Stryla