Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics

Vojkan Jaksic (1) , Yoshiko Ogata (2) , Claude-Alain Pillet (3, 4, 5) , Robert Seiringer (1)

1 Department of Mathematics and Statistics [Montréal]
2 Department of Mathematical Sciences
3 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
4 CPT - E5 Physique statistique et systèmes complexes
5 CPT - Centre de Physique Théorique - UMR 7332

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.

Mots clés: entropy production; quantum hypothesis testing; nonequilibrium statistical mechanics

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Vojkan Jaksic, Yoshiko Ogata, Claude-Alain Pillet, Robert Seiringer. Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics. Reviews in Mathematical Physics, 2011, 24 (6), pp.1-60. ⟨hal-00624487v2⟩