  Luttinger liquid theory of one-dimensional quantum systems ignores
exponentially weak backscattering of particles. This endows Luttinger liquids
with superfluid properties. The corresponding two-fluid hydrodynamic
description available at present applies only to Galilean-invariant systems,
whereas most experimental realizations of one-dimensional quantum liquids lack
Galilean invariance. Here we develop the two-fluid theory of such quantum
liquids. In the low-frequency limit the theory reduces to single-fluid
hydrodynamics. However, the absence of Galilean invariance brings about three
new transport coefficients. We obtain expressions for these coefficients in
terms of the backscattering rate.
