On the limit relation for the quantum relative entropy

TL;DR

This paper explores the asymptotic behavior of quantum relative entropy in reservoir models, extending previous results and providing new interpretations of the relationship between thermodynamic and informational entropy.

Contribution

It offers a new interpretation of the original conjecture and generalizes the asymptotic results to broader classes of quantum states.

Findings

Confirmed the asymptotic relation for a wider class of states

Provided a new conceptual framework for entropy in quantum reservoirs

Extended previous proofs to more general quantum models

Abstract

Recently, Di\'osi et al. (Int. J. Quant. Inf. 4, 99 (2006)) introduced a simple, yet very interesting model for reservoirs, in order to study the relationship between thermodynamic entropy production of a system and the corresponding von Neumann entropy (or informatic entropy, as it was called by the authors). They came up with a conjecture about the asymptotic behaviour of the state introduced in the model. The conjecture was proven later by Csisz\'ar et al. (J. Math. Phys. 48, 092102 (2007)). In this paper we give a different interpretation of the original question and extend the result to a collection of more general states.