  This paper considers the problem of data compression for dependent quantum
systems. It is the second in a series under the same title. As in the previous
paper, we are interested in Lempel--Ziv encoding for quantum Gibbs ensembles.
Here, we consider the canonical ideal lattice Bose- and Fermi-ensembles. We
prove that as in the case of the grand canonical ensemble, the (limiting) von
Neumann entropy rate $h$ can be assessed, via the classical Lempel--Ziv
universal coding algorithm, from a single eigenvector of the density matrix.
