  Dissipative quantum systems are frequently described within the framework of
the so-called "system-plus-reservoir" approach. In this work we assign their
description to the Maximum Entropy Formalism and compare the resulting
thermodynamic properties with those of the well - established approaches. Due
to the non-negligible coupling to the heat reservoir, these systems are
non-extensive by nature, and the former task may require the use of
non-extensive parameter dependent informational entropies. In doing so, we
address the problem of choosing appropriate forms of those entropies in order
to describe a consistent thermodynamics for dissipative quantum systems.
Nevertheless, even having chosen the most successful and popular forms of those
entropies, we have proven our model to be a counterexample where this sort of
approach leads us to wrong results.
