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Recently1 we have shown that a "global phase space" (GPS) approach provides valuable understanding of the long-time coherence and Einstein-Podolsky-Rosen entanglement of a Bose-Einstein Condensate (BEC) trapped in a double-well optical lattice ("BEC dimer"). In particular, the GPS approach allows one to distinguish purely quantum effects from those which are captured by semi-classical methods.The GPS approach in Ref. (1) was applied in the limit of zero dissipation. After reviewing the key results in this limit, we extend the approach to allow for dissipation and again compare the results with relevant experiments. Surprisingly, although consistent with some prior exploratory studies, we find that dissipation can actually enhance coherence in certain instances, particularly around self-trapped modes, corresponding to fixed points in the classical phase space. We explain a number of interesting features of this enhancement and argue that, in spatially extended systems (corresponding to multi-well optical lattices), these localized, self-trapped modes may also play a role in enhancing coherence.* With Ted Pudlik (BU), Holger Hennig (Harvard), and Dirk WItthaut (MPIDS-Göttingen) Holger Hennig, Dirk Witthaut, and David K. Campbell, Phys. Rev. A 86, 051640 [R] 2012.