Viscosity and dissipative hydrodynamics from effective field theory

TL;DR

The paper formulates dissipative hydrodynamics from a classical Schwinger-Keldysh (CTP) effective action for an open system, introducing a two-time-axis structure that captures environment-induced energy exchange. By constructing a gradient-expanded CTP Lagrangian with cross-axis couplings, the authors derive an energy-momentum balance that becomes approximately conserved near hydrodynamic equilibrium and recover Navier-Stokes-type dynamics; in this setup the shear viscosity vanishes while the bulk viscosity is determined by the effective action. A key finding is that entropy production is not automatically positive and requires additional constraints on the action, except in special limits. The work provides a principled variational framework for dissipative hydrodynamics within an EFT, clarifying how environment coupling and symmetry considerations shape transport coefficients and thermodynamics, and outlining directions to connect with microscopic unitary theories.

Abstract

With the goal of deriving dissipative hydrodynamics from an action, we study classical actions for open systems, which follow from the generic structure of effective actions in the Schwinger-Keldysh Closed-Time-Path formalism with two time axes and a doubling of degrees of freedom. The central structural feature of such effective actions is the coupling between degrees of freedom on the two time axes. This reflects the fact that from an effective field theory point of view, dissipation is the loss of energy of the low-energy hydrodynamical degrees of freedom to the integrated-out, UV degrees of freedom of the environment. The dynamics of only the hydrodynamical modes may therefore not posses a conserved stress-energy tensor. After a general discussion of the CTP effective actions, we use the variational principle to derive the energy-momentum balance equation for a dissipative fluid from an effective Goldstone action of the long-range hydrodynamical modes. Despite the absence of conserved energy and momentum, we show that we can construct the first-order dissipative stress-energy tensor and derive the Navier-Stokes equations near hydrodynamical equilibrium. The shear viscosity is shown to vanish in the classical theory under consideration, while the bulk viscosity is determined by the form of the effective action. We also discuss the thermodynamics of the system and analyse the entropy production.