ar X iv : m at h - ph / 0 30 50 16 v 1 8 M ay 2 00 3 The von Neumann entropy and information rate for integrable quantum Gibbs ensembles , 2

This paper considers the problem of data compression for dependent quantum systems. It is the second in a series under the same title which began with [6] and continues with [12]. As in [6], we are interested in Lempel–Ziv encoding for quantum Gibbs ensembles. Here, we consider the canonical ideal lattice Boseand 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 ψ of the density matrix ρ.