Non-Gaussian fluctuation dynamics in relativistic fluids

TL;DR

This paper investigates the non-Gaussian fluctuation dynamics in relativistic hydrodynamics near the QCD critical point, deriving evolution equations for non-Gaussian correlators relevant for heavy-ion collision experiments.

Contribution

It introduces a framework for analyzing non-Gaussian fluctuations in relativistic fluids, focusing on slow modes near the critical point, and derives their evolution equations in a hydrodynamic setting.

Findings

Derived evolution equations for non-Gaussian correlators in relativistic hydrodynamics.

Identified specific terms related to pressure fluctuations and flow in the full hydrodynamic case.

Compared with static diffusion, highlighting the effects of hydrodynamic flow on fluctuations.

Abstract

We consider non-equilibrium evolution of non-Gaussian fluctuations within relativistic hydrodynamics relevant for the QCD critical point search in heavy-ion collision experiments. We rely on the hierarchy of relaxation time scales, which emerges in the hydrodynamic regime near the critical point, to focus on the slowest mode such as the fluctuations of specific entropy, whose equilibrium magnitude, non-Gaussianity and typical relaxation time are increasing as the critical point is approached. We derive evolution equations for the non-Gaussian correlators of this diffusive mode in an arbitrary relativistic hydrodynamic flow. We compare with the simpler case of the stochastic diffusion on a static homogeneous background and identify terms which are specific to the case of the full hydrodynamics with pressure fluctuations and flow.