Two-fluid dynamics for a Bose-Einstein condensate out of local equilibriumwith the noncondensate

We extend our recent work on the two-fluid hydrodynamics of a Bose-condense d gas by including collisions involving both condensate and noncondensate a toms. These collisions are essential for establishing a state of local ther modynamic equilibrium between the condensate and noncondensate. Our theory is more general than the usual Landau two-fluid theory, to which it reduces in the appropriate limit, in that it allows one to describe situations in which a state of complete local equilibrium between the two components has not been reached. The exchange of atoms between the condensate and nonconde nsate is associated with a new relaxational mode of the gas.