We study the influence of entanglement on the relation between the
statistical entropy of an open quantum system and the heat exchanged with a low
temperature environment. A model of quantum Brownian motion of the
Caldeira-Leggett type - for which a violation of the Clausius inequality has
been stated by Th.M. Nieuwenhuizen and A.E. Allahverdyan [Phys. Rev. E 66,
036102 (2002)] - is reexamined and the results of the cited work are put into
perspective. In order to address the problem from an information theoretical
viewpoint a model of two coupled Brownian oscillators is formulated that can
also be viewed as a continuum version of a two-qubit system. The influence of
an additional internal coupling parameter on heat and entropy changes is
described and the findings are compared to the case of a single Brownian
particle.Comment: 10 pages, 11 figure