Recent developments in relativistic hydrodynamic fluctuations

TL;DR

This paper reviews recent advances in the theory of relativistic hydrodynamic fluctuations, covering stochastic hydrodynamics, hydro-kinetics, and effective field theory approaches, highlighting their developments and differences.

Contribution

It provides a comprehensive overview and comparison of three recent theoretical frameworks for relativistic hydrodynamic fluctuations.

Findings

Comparison of stochastic hydrodynamics, hydro-kinetics, and effective field theory.

Highlighting recent progress in each framework.

Clarification of the relationships among different approaches.

Abstract

The study of thermal fluctuations in relativistic hydrodynamics has led to numerous important developments in the last decade. We present a bird's eye view of the recent advances on the theory of fluctuations on three fronts; stochastic hydrodynamics, hydro-kinetics where fluctuations are included as additional modes that satisfy deterministic evolution equations, and effective field theory formulation of relativistic hydrodynamics. We compare and contrast these different but complimentary frameworks and highlight various recent progresses in each of them.