Viscosity and dissipative hydrodynamics from effective field theory
  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.
