  We use the maximum information principle to include particle-interaction into
the grand-canonical theory of BECs. The inclusion of the particle-interaction
elucidates why thermodynamic calculations for BECs by the grand-canonical
ensemble for the non-interacting case are in coincidence with up to date
experimental results. However, in our generalized theory we can show that a BEC
experiences a real and abrupt phase-transition in contrast to the smooth
phase-transition predicted by the non-interacting grand-canonical ensemble. In
addition, we discuss possible effects due to a thermal environment and the
experimental probing from a general point of view.
