Consistency of some well-posed five-field theories of dissipative relativistic fluid dynamics
Heinrich Freistuhler
TL;DR
The paper investigates the consistency of causal, hyperbolic five-field relativistic dissipative fluid theories (the FTBDNK family) by focusing on Eulerian gradient shifts that generate the orbit $\mathcal{E}_5(L)$ from the Landau-Lifshitz description. It proves that elements of $\mathcal{E}_5(L)$ are $O(ε^2)$-equivalent to Landau-Lifshitz, produce $O(ε^3)$ excess entropy, and preserve heterogeneous local thermodynamic equilibria, while admitting regular heteroclinic shock profiles for small amplitude shocks. It also develops barotropic and Eckart variants, showing second-order equivalence and LTE compatibility extend to these cases, and provides a constructive shock-profile result via a center-manifold analysis. Collectively, these results establish robust structural consistency for a broad class of dissipative relativistic fluids, including sane entropy production and physically meaningful equilibria across small shocks. The work thus strengthens the theoretical foundation for causally consistent relativistic dissipative hydrodynamics in applications requiring stable shock behavior and LTE adherence.
Abstract
Within the FTBDNK family of formulations of relativistic Navier-Stokes (H. Freistühler and B. Temple, Proc. R. Soc. A 470, 20140055 (2014), Proc. R. Soc. A 473 (2017), 20160729; F. S. Bemfica, M. Disconzi, and J. Noronha, Phys. Rev. D 98, 104064 (2018), Phys. Rev. D 100, 104020 (2019); P. Kovtun, J. High Energy Phys. 2019, 034 (2019)), this paper collects some consistency properties for certain causal hyperbolic five-field theories obtained from the Landau-Lifshitz formulation via Eulerian gradient shifts, a family, EGS(L), of models that slightly generalize a class identified in H. Freistühler, J. Math.\ Phys. 61, 033101 (2020). With $ε$ the magnitude of the dissipation coefficients that quantify viscosity and heat conduction, the paper shows that any element of EGS(L) is $O(ε^2)$ equivalent to the Landau-Lifshitz formulation, has an $O(ε^3)$ excess entropy production, represents heterogeneous local thermodynamic equilibria cleanly, and admits regular heteroclinic profiles for all shock waves of sufficiently small amplitude.