We comment on a formulation of quantum statistical mechanics, which
incorporates the statistical inference of Shannon.
Our basic idea is to distinguish the dynamical entropy of von Neumann, H=−kTrρ^lnρ^, in terms of the density matrix ρ^(t),
and the statistical amount of uncertainty of Shannon, S=−k∑npnlnpn, with pn= in the representation where the total
energy and particle numbers are diagonal. These quantities satisfy the
inequality S≥H. We propose to interprete Shannon's statistical inference
as specifying the {\em initial conditions} of the system in terms of pn. A
definition of macroscopic observables which are characterized by intrinsic time
scales is given, and a quantum mechanical condition on the system, which
ensures equilibrium, is discussed on the basis of time averaging.
An interesting analogy of the change of entroy with the running coupling in
renormalization group is noted. A salient feature of our approach is that the
distinction between statistical aspects and dynamical aspects of quantum
statistical mechanics is very transparent.Comment: 16 pages. Minor refinement in the statements in the previous version.
This version has been published in Journal of Phys. Soc. Jpn. 71 (2002) 6