First-order relativistic hydrodynamics with an information current

TL;DR

This paper introduces the concept of an information current in relativistic first-order hydrodynamics, enabling a covariant, stable, and causal formulation that applies across various physical phenomena and influences fluctuation correlations.

Contribution

It is the first to define an information current within relativistic hydrodynamics, advancing a covariant, stable, and causal theoretical framework based on thermodynamic principles.

Findings

Information currents enable frame-independent correlation functions.

Chiral hydrodynamics shows handedness-dependent excitation probabilities.

The approach applies to phenomena from electric conduction to elasticity.

Abstract

We show that it is possible to define a timelike future-directed information current within relativistic first-order hydrodynamics. This constitutes the first step toward a covariantly stable and causal formulation of first-order fluctuating hydrodynamics based on thermodynamic principles. We provide several explicit examples of first-order theories with an information current, covering many physical phenomena, ranging from electric conduction to viscosity and elasticity. We use these information currents to compute the corresponding equal-time correlation functions, and we find that the physically relevant (equal-time) correlators do not depend on the choice of the hydrodynamic frame as long as the frame leads to causal and stable dynamics. In the example of chiral hydrodynamics, we find that circularly polarized shear waves have different probabilities of being excited depending on their handedness, generating net helicity in chiral fluids.