  We consider non-Fermi liquids in which the inelastic scattering rate has an
intrinsic particle-hole asymmetry and obeys $\omega/T$ scaling. We show that,
in contrast to Fermi liquids, this asymmetry influences the low-temperature
behaviour of the thermopower even in the presence of impurity scattering.
Implications for the unconventional sign and temperature dependence of the
thermopower in cuprates in the strange metal (Planckian) regime are emphasized.
