Information geometry and reduced quantum description
The framework of the so-called statistical dynamics, developed by the present author, is applied to the quantum version of non-equilibrium statistical mechanics, where the ``slow'' variables are represented by selfadjoint operators, not necessarily bounded, on a Hilbert space. The subject of study is the quantum dynamics of a system with two time-scales, having discrete time and unbounded slow variables, under a useful set of axioms, it is argued that the Kubo susceptibility tensor is the appropriate generalizations of the Fisher information metric on the set of density matrices. The geometric picture of reduced quantum dynamics (via suitable projection methods) is extended to some unbounded cases and shown to be related to a contraction in the Bogoliubov norm.
scientific article; zbMATH DE number 1090458
scientific article