Relativistic fluctuating hydrodynamics with memory functions and colored noises

TL;DR

This paper develops a formulation of relativistic fluctuating hydrodynamics that emphasizes causality and non-linearity, deriving equations with colored noises consistent with fluctuation-dissipation relations for improved numerical simulations.

Contribution

It introduces a new formulation of relativistic fluctuating hydrodynamics that incorporates memory functions and colored noises, ensuring causality and non-linearity are properly modeled.

Findings

Derived integral and differential forms of constitutive equations

Showed noises are colored in integral form but white in differential form

Provided equations suitable for numerical implementation

Abstract

Relativistic dissipative hydrodynamics including hydrodynamic fluctuations is formulated by putting an emphasis on non-linearity and causality. As a consequence of causality, dissipative currents become dynamical variables and noises appeared in an integral form of constitutive equations should be colored ones from fluctuation-dissipation relations. Nevertheless noises turn out to be white ones in its differential form when noises are assumed to be Gaussian. The obtained ifferential equations are very useful in numerical implementation of relativistic fluctuating hydrodynamics.