Emergence of thermodynamic properties in quantum pure states. I. Foundations (original) (raw)

Investigation on foundational aspects of quantum statistical mechanics are recently entered in a renaissance period due to novel intuitions from quantum information theory and an increasing attention to the dynamical aspects of single quantum systems. In the present contribution a simple but effective theoretical framework to clarify the connections between the pure mechanical description and the thermodynamic characterization of the equilibrium state of a single quantum system is presented. A salient feature of our approach is the very transparent distinction between the statistical aspects and the dynamical aspects of quantum statistical mechanics. On the one hand equilibrium properties of quantum system appear to depend on the details of the initial state due to the abundance of constants of the motion in the Schroedinger dynamics. On the other hands the study of the probability distributions of some functions, such as the entropy or the equilibrium state of a subsystem, in statistical ensembles of pure states reveals the crucial role of typicality as the bridge between macroscopic thermodynamics and microscopic quantum dynamics. The relation between the introduced ensembles, the properties of the single system and the standard quantum statistical description is discussed throughout the presentation. Finally we point out the conditions under which a meaningful thermodynamical characterization of an isolated quantum system in a pure state can be given.