  Using effective field theory methods, we calculate the low-temperature phonon
thermal partition function for a generic superfluid, thus providing the leading
thermal corrections to a superfluid's equation of state, thermodynamic
quantities, and conserved currents. We confirm the correctness of the classic
two-fluid model by matching to the effective field theory for that model. Where
there is an overlap, our results agree with those of Carter and Langlois, which
were derived by different methods. We also discuss generalizations and special
cases, including the non-relativistic limit and the conformal superfluid.
