  New, superfluid specific additive integral of motion is found. This
facilitates investigation of general thermodynamic equilibrium conditions for
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.
