Non-Gaussian fluctuations in relativistic hydrodynamics: Confluent equations for three-point correlations

TL;DR

This paper develops a covariant formalism for the evolution of non-Gaussian fluctuations in relativistic hydrodynamics, including equations for correlators of all hydrodynamic variables.

Contribution

It introduces a novel relativistic, covariant formalism for nonlinear stochastic hydrodynamics that captures non-Gaussian fluctuations and their correlations.

Findings

Derived deterministic equations for non-Gaussian fluctuation evolution.

Unified multi-component matrix form for stochastic hydrodynamics.

Formalism is covariant under SO(3) rotations in the local Landau frame.

Abstract

We derive deterministic equations for the evolution of non-Gaussian fluctuations in relativistic stochastic hydrodynamics. This is achieved by defining the average local Landau frame and corresponding fluctuating hydrodynamic variables. Fully nonlinear stochastic hydrodynamics is expressed in a unified multi-component matrix form. A novel relativistic formalism, also manifestly covariant under SO(3) rotations of the local spatial basis in the average local Landau frame, is introduced. The equations describe correlators of all hydrodynamic variables, including fluctuating velocity (or momentum density) -- a nontrivial problem in relativistic hydrodynamics.