Quantum hypothesis testing and non-equilibrium statistical mechanics (Q2911997)

The mathematical theory of non-equilibrium quantum statistical mechanics has developed rapidly in recent years. The research efforts are centered around the theory of entropic fluctuations and these developments are also concerned in this paper. As it is known there is a close interplay between information theory and statistical mechanics. One of the deepest links is provided by the theory of large deviations. In this paper, the authors attempt to interpret recent results in non-equilibrium statistical mechanics in terms of quantum information theory. They prove some results and elaborate the relations between quantum hypothesis testing and non-equilibrium statistical mechanics.NEWLINENEWLINEThis paper consists of 8 sections. After an introduction in Section 2, they present a review with necessary proofs of results from large deviation theory. Then, Section 3 gives existing results in quantum hypothesis testing of finite quantum systems. After this, the description of non-equilibrium statistical mechanics of finite quantum systems with quantum hypothesis testing is discussed in Subsection 4.5. Section 5 presents results of modular theory. The next two sections are devoted to quantum hypothesis testing and non-equilibrium statistical mechanics of infinitely extended quantum systems described by \(W^*\)-algebras and \(W^*\)-dynamical systems. The last section describes several physical models for which the existence of the large deviation functionals is proven.