Thermodynamics of Superfluidity

A new superfluid specific additive integral of motion is found. This facilitates investigation of the general thermodynamic equilibrium conditions of a superfluid. The analysis is performed in an extended space of thermodynamic variables containing (along with the usual thermodynamic coordinates such as pressure and temperature) superfluid velocity and momentum density. The equilibrium stability conditions lead to thermodynamic inequalities which replace the Landau superfluidity criterion at finite temperatures.