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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., Comment: 32 pages, 12 figures

Shannon entropies of one- and two-electron atomic structure factors in the position and momentum representations are used to examine the behavior of the off-diagonal elements of density matrices with respect to the uncertainty principle and to analyze the effects of electron correlation on off-diagonal order. We show that electron correlation induces off-diagonal order in position space which is characterized by larger entropic values. Electron correlation in momentum space is characterized by smaller entropic values as information is forced into regions closer to the diagonal. Related off-diagonal correlation functions are also discussed.

Mutual information and information entropies in momentum space are proposed as measures of the non-local aspects of information. Singlet and triplet state members of the helium isoelectronic series are employed to examine Coulomb and Fermi correlation, and their manifestations, in both the position and momentum space mutual information measures. The triplet state measures exemplify that the magnitude of the spatial correlations relative to the momentum correlations, depends on, and may be controlled by the strength of the electronic correlation. Examination of one and two-electron Shannon entropies in the triplet state series yields a crossover point, which is characterized by a localized momentum density. The mutual information density in momentum space illustrates that this localization is accompanied by strong correlation at small values of $p$., Comment: 21 pages, 8 figures