An action principle for dissipative fluid dynamics

Abstract

Fluid dynamics is the universal theory of low-energy excitations around equilibrium states, governing the physics of long-lived modes associated with conserved charges. Historically, fluid dynamics has been formulated at the level of equations of motion, in terms of a local fluid velocity and thermodynamic quantities. In this thesis, we describe a new formulation of fluid dynamics in terms of a path integral, which systematically encodes the effects of thermal and quantum fluctuations. In our formulation, the dynamical degrees of freedom are Stuckelberg-type fields associated to the conserved quantities, which are subject to natural symmetry considerations, and the time evolution of the path integral is along the closed-time contour. Our formulation recovers the standard hydrodynamics, including the expected constraints from thermodynamics and the fluctuation-dissipation theorem, as well as an additional non-linear generalization of the Onsager relations. We demonstrate an emergent supersymmetry in the "classical statistical" limit of our theory. For the non-linear fluid, the formalism is encoded in a non-trivial differential geometric structure, with a non vanishing torsion tensor required to recover the correct physics of the most general fluid. Finally, we discuss progress in obtaining a holographic derivation of the action formulation at the ideal level, in which the low energy degrees of freedom emerge naturally as the relative embedding of the boundary and horizon hypersurfaces.