  The effects of bath coupling on an interacting two-particle quantum system
are studied using tools from information theory. Shannon entropies of the one
(reduced) and two-particle distribution functions in position, momentum and
separable phase-space are examined. Results show that the presence of the bath
leads to a delocalization of the distribution functions in position space, and
a localization in momentum space. This can be interpreted as a loss of
information in position space and a gain of information in momentum space. The
entropy sum of the system, in the presence of a bath, is shown to be dependent
on the strength of the interparticle potential and also on the strength of the
coupling to the bath. The statistical correlation between the particles, and
its dependence on the bath and interparticle potential, is examined using
mutual information. A stronger repulsive potential between particles, in the
presence of the bath, yields a smaller correlation between the particles
positions, and a larger one between their momenta.
