Fluctuations in Relativistic Causal Hydrodynamics

TL;DR

This paper extends the calculation of hydrodynamic fluctuations to second and third order causal relativistic hydrodynamics, showing that correlation functions are model-independent and similar across different theories.

Contribution

It provides a unified framework for calculating hydrodynamic fluctuations in various causal hydrodynamics models, including second and third order theories.

Findings

Correlation functions are model-independent across different hydrodynamics theories.

Qualitative behavior of fluctuations remains consistent among models.

Causal hydrodynamics yields similar fluctuation correlations as relativistic Navier-Stokes.

Abstract

Formalism to calculate the hydrodynamic fluctuations by applying the Onsager theory to the relativistic Navier-Stokes equation is already known. In this work, we calculate hydrodynamic-fluctuations within the framework of the second order hydrodynamics of M\"{u}ller, Israel and Stewart and its generalization to the third order. We have also calculated the fluctuations for several other causal hydrodynamical equations. We show that the form for the Onsager-coefficients and form of the correlation-functions remains same as those obtained by the relativistic Navier-Stokes equation and it does not depend on any specific model of hydrodynamics. Further we numerically investigate evolution of the correlation function using the one dimensional boost-invariant (Bjorken) flow. We compare the correlation functions obtained using the causal hydrodynamics with the correlation-function for the relativistic Navier-Stokes equation. We find that the qualitative behavior of the correlation-functions remain same for all the models of the causal hydrodynamics.