Heat Capacity Anomalies of Superfluid 4He under the Influence of a Counterflow near Tl

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 Tl, 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. [S0031-9007(96)00890-3]