  The low energy and finite temperature excitations of a $d+1$-dimensional
system exhibiting superfluidity are well described by a hydrodynamic model with
two fluid flows: a normal flow and a superfluid flow. In the vicinity of a
quantum critical point, thermodynamics and transport in the system are expected
to be controlled by the critical exponents and by the spectrum of irrelevant
deformations away from the quantum critical point. Here, using gauge-gravity
duality, we present the low temperature dependence of thermodynamic and charge
transport coefficients at first order in the hydrodynamic derivative expansion
in terms of the critical exponents. Special attention will be paid to the
behavior of the charge density of the normal flow in systems with emergent
infrared conformal and Lifshitz symmetries, parameterized by a Lifshitz
dynamical exponent $z>1$. When $1\leq z<d+2$, we recover ($z=1$) and extend
($z>1$) previous results obtained by relativistic effective field theory
techniques. Instead, when $z>d+2$, we show that the normal charge density
becomes non-vanishing at zero temperature. An extended appendix generalizes
these results to systems that violate hyperscaling as well as systems with
generalized photon masses. Our results clarify previous work in the holographic
literature and have relevance to recent experimental measurements of the
superfluid density on cuprate superconductors.
