Reasoning about quantum systems at the macroscopic level

In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as to quantum state reconstruction on the basis of incomplete data. There are two appendices in which I outline how generalised canonical distributions link to the conventional formulation of statistical mechanics, and how classical probability calculus emerges at the macroscopic level.