Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
  We extend the mathematical theory of quantum hypothesis testing to the general $W^*$-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time. 
V. Jaksic, Y. Ogata, C.-A. Pillet, R. Seiringer
math-ph cs.IT math.IT math.MP quant-ph