We derive a damping mechanism in the open quantum system description of Bose-Einstein condensates. It stems from previously neglected terms in the derivation of the stochastic projective Gross-Pitaevskii equation (SPGPE), accounting for a nonlinear evaporation of particles from the coherent into the incoherent region. We demonstrate that the mechanism, while so far assumed to be of minor importance, is comparable in strength to the widely employed number damping. We also provide a simplified (pseudo)local and a dimensionally reduced form of this evaporative damping. The process completes the SPGPE description of ultracold Bose gases giving a full first-principles picture of their evolution at finite temperature.

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• Bose-Einstein condensates
• Cold atoms & matter waves
• Collective effects in atomic physics
• Phase space methods