Irreversibility in Collapse-Free Quantum Dynamics and the Second Law of   Thermodynamics
  Proposals to solve the problems of quantum measurement via non-linear CPT-violating modifications of quantum dynamics are argued to provide a possible fundamental explanation for the irreversibility of statistical mechanics as well. The argument is expressed in terms of collapse-free accounts. The reverse picture, in which statistical irreversibility generates quantum irreversibility, is argued to be less satisfactory because it leaves the Born probability rule unexplained. 
M. B. Weissman