# Hydro-kinetics

Stochastic fluctuations in out-of-equilibrium systems

The **fluctuation dissipation theorem** dictates that any dissipative system exhibits **stochastic fluctuations** thanks to the microscopic degrees of freedom. The remarkable property of QGP
is that it is well described by macroscopic theory of **viscous hydrodynamics**, despite its microscopic volume.
However, **thermal fluctuations** have been so far neglected in most of
heavy-ion model studies, because of difficulty of implementing stochastic noise in hydrodynamic
simulations.

A novel approach in describing effect of **hydrodynamic fluctuations** has been pioneered in our
papers on **hydro-kinetics**, where we derived deterministic evolution equations for the **two-point
correlation functions** of fluid fields, which are equivalent to
nonlinear hydrodynamics with noise. We used the hydro-kinetic equations to analyse thermal fluctuations
for a Bjorken expansion, evaluating the contribution of thermal noise from the earliest moments and at late times.

Recently the approach was generalized to arbitrary
background flows, which could be implemented in realistic heavy-ion simulations. Inclusion
of such dynamical fluctuations is particularly important for the searches of the **critical point** in
QCD phase diagram, with experimental efforts currently underway at Relativistic Heavy Ion
Collider (RHIC) at BNL.