Stochastic hydrodynamics and hydro-kinetics: Similarities and differences

TL;DR

This paper compares stochastic hydrodynamics and hydro-kinetics, highlighting their similarities and differences, especially in how they handle noise and correlations in the evolution of conserved charge fluctuations.

Contribution

It provides a detailed comparison between stochastic hydrodynamics and hydro-kinetics, emphasizing their divergence under colored noise conditions and the role of higher-order correlations.

Findings

White noise approaches agree in both methods.

Colored Catteneo noise causes divergence due to higher-order correlations.

Causal evolution effects are significant in colored noise scenarios.

Abstract

The hydro-kinetic formalism has been used as a complementary approach to solving the Stochastic Differential Equations (SDE) corresponding to noisy hydrodynamics. The hydro-kinetic formalism consists of a deterministic set of relaxation type equations that tracks the evolution of 2-point correlation functions of stochastic hydrodynamic quantities. Hence they are comparatively easier to solve than the SDEs, which are computationally intensive and need to deal with arbitrarily large gradients. This work compares the two approaches for the propagation and diffusion of conserved charge fluctuations in the Bjorken hydrodynamic model. For white noise, the two approaches agree. For colored Catteneo noise, which is causal, the two approaches diverge. This is because white noise only induces two-point correlations, while Catteneo noise also induces higher-order correlations. This difference is quantified from the effects of causal evolution and influence from higher-order correlations induced by the Catteneo noise.