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We derive a non-equilibrium finite-temperature kinetic theory for a binarymixture of two interacting atomic Bose-Einstein condensates and use it toexplore the degree of hydrodynamicity attainable in realistic experimentalgeometries. Based on the standard separation of timescale argument of kinetictheory, the dynamics of the condensates of the multi-component system are shownto be described by dissipative Gross-Pitaevskii equations, self-consistentlycoupled to corresponding Quantum Boltzmann equations for the non-condensateatoms: on top of the usual mean field contributions, our scheme identifies atotal of eight distinct collisional processes, whose dynamical interplay isexpected to be responsible for the systems equilibration. In order to providetheir first characterization, we perform a detailed numerical analysis of therole of trap frequency and geometry on collisional rates for experimentallyaccessible mixtures of $^{87}$Rb-$^{41}$K and $^{87}$Rb-$^{85}$Rb, discussingthe extent to which the system may approach the hydrodynamic regime with regardto some of those processes, as a guide for future experimental investigationsof ultracold Bose gas mixtures.

A Non-Equilibrium Kinetic Theory for Trapped Binary Condensates