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

TL;DR

The paper demonstrates that linear instabilities of first-order hydrodynamics, previously established for Lorentzian fluids with positive entropy production, persist when extended to non-Lorentzian (Bargmann and Carrollian) fluids, indicating that these instabilities are tied to the gradient-truncation rather than to Lorentz symmetry alone.By constructing explicit constitutive relations across Lorentzian, Bargmann, and Carrollian fluids and analyzing frame choices (Landau, Eckart, and general), it identifies stable combinations (e.g., Bargmann-Eckart) and widespread instabilities in other frames, including Carrollian cases.The work provides a detailed linear stability analysis across the full spectrum of first-order hydrodynamics, including $c o o ext{infty}$ and $c o0$ contractions, and even a general frame without boost symmetry, highlighting the sensitivity of stability to both symmetry and frame choice.These findings motivate considering beyond-first-order theories (e.g., Muller-Israel-Stewart-type formalisms) or relaxed entropy-current constraints to obtain well-behaved hydrodynamics, and they connect to flat-space holography and Carrollian physics as potential avenues for consistent effective descriptions.

Abstract

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. We also present a complete linearised analysis of the full spectrum of first order Carrollian hydrodynamics. Furthermore, we show that even in a fluid without boost symmetry present, instabilities can occur. These results provide evidence that the unphysical instabilities are symptoms of first order hydrodynamics, rather than a special feature of Lorentzian fluids.

Figures (2)

• Figure 1: (LEFT) The pole structure of the transverse fluctuations around the static $(P_i =0)$, homogeneous configuration of a Lorentzian, Bargmann or Carollian fluid in general frame. The unstable mode is moved towards $\omega \to +i\infty$ and is removed from the spectrum as one continuously tunes the transport coefficient towards the Landau frame (for Lorentzian and Carrollian fluid) and Eckart frame (for Bargmann fluid). (RIGHT) This panel illustrates the unstable mode in the Landau frame of a Carrollian or a Lorentzian fluid at $P_i \ne 0$, which moves down from $\omega \to +i\infty$ as we move away from $P_i = 0$ configuration. This pole is absent in the Eckart frame of the Bargmann fluid.
• Figure 2: In this table, we showcase an overview of instabilities of first order hydrodynamics, including our results. Here $P_{i}:=T^{0}_{\;\;\,i}$ denotes momentum density, which can be made zero or non-zero by performing a boost.