One of the problems may be that thermodynamics is rigorous only in the thermodynamic limit. In small systems fluctuations play a major role and become comparable in magnitude to the thermal averages. Also, thermal equilibrium requires typically coupling to a thermostat unless one is interested in the experimentally hard to realize microcanonical situation. Thermal contact is however something you may want to avoid in the case of ultra-cold gases of a few atoms only. Finally, if there is interaction on a length-scale comparable with the system size thermodynamics is no more applicable. 

I am pretty sure it has been decided that N can be pretty small and still be awfully good for a thermodynamics limit so that is not the problem but the role of fluctuations and hydrodyanmics "breaking" is considered a real issue with formal thermodynamics expansions.  In some sense, this is an old problem since Dorfman and Cohen showed that the formal expansions diverged back in the 60's.  The field theory calculations are rather formal so you basically have the choice of believing them when they work and trying something else when they don't.  Another long term problem waiting resolution. 

There is a cottage industry in applying formal hydro/thermo expansions to such cold gas clouds and seeking the coefficients from field theory or other many body quantum methods.  No one has ever given a solid foundation for quantum statistical mechanics so it is hard to say for what systems it is valid but it is certainly a tool to generate calculations and, to low order, there is something well approximated by hydrodynamics for the excitations of these gases.  Phase diagrams for strongly interacting fermions are generated and applied and tested against these systems.  I have a feeling that these systems are always described by many body quantum wavefunctions (until measured with a destructive laser pulse) that are typically nonthermal and so in a persistent fashion.  I haven't carefully looked at the article yet but sounds like it possibly could support such a position.  I'd like to know if anyone knows more about theory in this direction.