  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.
