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A Bose-Einstein condensate is a state with macroscopic occupation of a one-particle mode. A phase-selected mean-field description can use $⟨\psi ⟩\ne 0$, while a fixed-number finite-volume state need not have a nonzero field expectation. Bose-Einstein condensation and superfluidity are related but distinct notions; long-wavelength phase fluctuations can invalidate a uniform condensate saddle in low dimensions.

A superfluid exhibits superfluidity, with phase stiffness and a phase-gradient current. In an appropriate ordered or quasi-ordered regime it supports low-speed flow without viscous dissipation, and its long-wavelength Goldstone boson has a sound-like dispersion. True thermodynamic phase selection and Bose-Einstein condensation need separate infrared conditions.

Superfluidity is a quantum-fluid response with phase stiffness and flow without viscous dissipation in an appropriate low-speed regime. A superfluid supports a phase-gradient current; defects and excitations can limit that flow. Bose-Einstein condensation concerns macroscopic one-particle occupation and is a distinct criterion: the Gaussian phase stiffness theory can have divergent absolute-phase fluctuations while retaining a cost for gradients.