On thermal fluctuations and the generating functional in relativistic hydrodynamics

Understand

We discuss a real-time generating functional for correlation functions in dissipative relativistic hydrodynamics which takes into account thermal fluctuations of the hydrodynamic variables.

• Starting from the known form of these correlation functions in the linearized regime, we integrate to find a generating functional which we can interpret within the CTP formalism, provided the space-time and internal global symmetries are realized in a specific manner in the (r,a) sectors.
• We then verify that this symmetry realization, when implemented in an effective action for hydrodynamic fields in the (r,a) basis, leads to a consistent derivative expansion for the constitutive relations at the nonlinear level, modulo constraints associated with the existence of an equilibrium state.