Superfluid density of an open dissipative condensate

I calculate the superfluid density of a non-equilibrium steady state condensate of particles with finite lifetime. Despite the absence of a simple Landau critical velocity, a superfluid response survives, but dissipation reduces the superfluid fraction. I also suggest an idea for how the superfluid density of an example of such a system, i.e. microcavity polaritons, might be measured.