Effective Action for Relativistic Hydrodynamics: Fluctuations, Dissipation, and Entropy Inflow

Understand

We present a detailed and self-contained analysis of the universal Schwinger-Keldysh effective field theory which describes macroscopic thermal fluctuations of a relativistic field theory, elaborating on our earlier construction in arXiv:1511.07809.

• We write an effective action for appropriate hydrodynamic Goldstone modes and fluctuation fields, and discuss the symmetries to be imposed.
• The constraints imposed by fluctuation-dissipation theorem are manifest in our formalism.
• Consequently, the action reproduces hydrodynamic constitutive relations consistent with the local second law at all orders in the derivative expansion, and captures the essential elements of the eightfold classification of hydrodynamic transport of arXiv:1502.00636.