 ::I just read the article on entropy of mixing and double checked a couple of independent sources, and now understand that this formula for mixing presumes equal temperature of the two substances being mixed.  Didn't know that before now.  Thus, the entropy of mixing refers to distribution of particles into a steady-state particle mix. This is an entirely different use of the word entropy which does not involve thermodynamics.  Learning new things here. Nonetheless, as to thermodynamic entropy, it remains that dispersal of energy from warmer particles to cooler particles always represents an increase of entropy in a closed system, consistently with the Second Law. ...  