Stochastic fluctuations in relativistic fluids: causality, stability, and the information current

Understand

We develop a general formalism for introducing stochastic fluctuations around thermodynamic equilibrium which takes into account, for the first time, recent developments on the causality and stability properties of relativistic hydrodynamic theories.

• The method is valid for any covariantly stable theory of relativistic viscous fluid dynamics derived from a covariant maximum entropy principle.
• We illustrate the formalism with some applications, showing how it could be used to consistently introduce fluctuations in a model of relativistic heat diffusion, and in conformally invariant Israel-Stewart theory in a general hydrodynamic frame.
• The latter example is used to study the hydrodynamic frame dependence of the symmetric two-point function of fluctuations of the energy-momentum tensor.