Low-temperature thermal corrections to a superfluid's equation of state

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.