The von Neumann entropy and information rate for ideal quantum Gibbs ensembles

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...

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

We consider the generic model of a finite-size quantum electron system connected to two (temperature and particle) reservoirs. The quantum open system is driven out of equilibrium by the presence of both a temperature and a chemical potential differences between the two reservoirs. The nonequilibrium (NE) thermodynamical properties of such a quantum open system are studied for the steady state ...

Invariant Entropy and Complexity of Quantum States

The concept of entropy is fundamental for many branches of physics and other sciences dealing with systems which reveal a certain degree of complexity and disorder. As stressed in the monograph 1, ‘‘entropy is not a single concept but rather a family of notions". In relation to quantum theory, the mainstream of development is formed by four main overlapping lines. They can be referred to as the...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

A note on continuous ensemble expansions of quantum states

Generalizing the notion of relative entropy, the difference between a priori and a posteriori relative entropy for quantum systems is drawn. The former, known as quantum relative entropy, is associated with quantum states recognition. The latter—a posteriori relative quantum entropy is introduced and shown to be related with state reconstruction due to the following property: given a density op...