The Cabibbo-Kobayashi-Maskawa density matrices
  The flavor changing charged currents of the weak sector of the Standard Model are studied in the framework of a quantum statistical approach. The quantum superposition of same-type quarks, generated by the Cabibbo-Kobayashi-Maskawa matrix, is used to define three density matrices, one for each quark family. The properties of such density matrices are analyzed, in particular, the associated von Neumann entropy. It is proven that, due to the unitarity of the Cabibbo-Kobayashi-Maskawa matrix, the quantum mixtures of quarks resulting from the weak interaction do not increase entropy and, therefore, the violation of CP and T symmetries cannot be related to the second law of thermodynamics. 
Miguel C. N. Fiolhais
hep-ph