Is Bose-Einstein Condensation a First-Order Phase Transition?

[paweld]

I'm not absolutely sure whether condensation of ideal gas of bosons (without
any interactions) is a first order phase transition. Some people claim that it
isn't first order phase transition because the entropy of a system is continuous
function at critical temperature. According to me however this reasoning
doesn't work because below critical temperature the system ceases to be uniform.
In fact it is a mixture of liquid and gas phase. The liquid phase has zero enetropy
and molar volume and the total entropy of the system is entarly due to gas phase. The
entropy of a whole system is continuous at critical temperature beacuse it is
equal to molar entropy of gas phase times number of moles of gas phase
(number of moles of gas phase changes continuously) but it is true in case
of any transition.

 

[DrDu]

I don't think that the system ceases to be uniform if the underlying hamiltonian is homogeneous. Of course you can say that the condensate does not carry entropy but only the excited states but that is not a phase separation in strict sense.