First order non-Lorentzian fluids, entropy production and linear instabilities

Understand

In this note, we investigate linear instabilities of hydrodynamics with corrections up to first order in derivatives.

• It has long been known that relativistic (Lorentzian) first order hydrodynamics, with positive local entropy production, exhibits unphysical instabilities.
• We extend this analysis to fluids with Galilean and Carrollian boost symmetries.
• We find that the instabilities occur in all cases, except for fluids with Galilean boost symmetry combined with the choice of macroscopic variables called Eckart frame.