Thermodynamics of quantum Brownian motion with internal degrees of freedom: the role of entanglement in the strong-coupling quantum regime

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.