A new approach for the justification of ensembles in quantum statistical mechanics — II

The results of the first paper in this series are generalized to include spin, permutation symmetry, and time dependence. In particular, the question of time invariance of localness in the Heisenberg picture is discussed and it is conjectured that an operator that is initially local will remain local over time. In order to treat macroscopic systems, it is shown that the ensemble decomposition of the previous paper can be used to coarsegrain configuration space. Finally, a physical interpretation of the ensemble decomposition in terms of redundant macroscopic information is used to give a derivation of the generalized microcanonical average.This work was supported in part by research grants from the National Science Foundation and the U.S. Public Health Service. Some of the material in this paper is contained in a doctoral dissertation submitted by the author to the University of Oregon (1969).