Consistent inclusion of fluctuations in first-order causal and stable relativistic hydrodynamics

Abstract

We construct, for the first time, a Bemfica-Disconzi-Noronha-Kovtun (BDNK) theory for linear stochastic fluctuations, which is proved to be mathematically consistent, causal, and covariantly stable. The Martin-Siggia-Rose action is shown to be bilocal in most cases, and the noise is not white. The presence of nonhydrodynamic modes induces long-range correlations in the primary fluid variables (temperature, chemical potential, and flow velocity). However, correlators of conserved densities remain localized in space, and coincide with those calculated within fluctuating Isreal-Stewart theory. We show that, in some cases, there is a nonlocal change of variables that maps the Israel-Stewart action into the BDNK action.

arXiv comment20 pages, 1 figure, published on PRD (see https://journals.aps.org/prd/abstract/10.1103/PhysRevD.109.125002)

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Cited by in corpus (4)

• The stochastic relativistic advection diffusion equation from the Metropolis algorithm
• Modelling stochastic fluctuations in relativistic kinetic theory
• Extending Israel-Stewart theory: Causal bulk viscosity at large gradients
• Thermodynamic stability of superflows in General Relativity and Newtonian gravity