Heat capacity anomalies of superfluid He-4 under the influence of a counterflow near T-lambda

We present a thermodynamic treatment of superfluid helium in the presence of an applied heat current, Q, which produces a counterflow velocity W→. We show that the heat capacity can be expressed in terms of the dependence of the superfluid density on W→. Near Tλ, both mean field theory and renormalization group theory give a divergent heat capacity with an exponent of 0.5 at a depressed transition temperature. In contrast, if W→ rather than Q is held constant, the heat capacity remains finite.