Viscosity and dissipative hydrodynamics from effective field theory

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 stressenergy 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. CONTENTS

Off-shell hydrodynamics from holography

“…We will leave its discussion and the full evaluation of (1.7) elsewhere. Hydrodynamical actions based on doubled X a degrees of freedom discussed here have also been discussed recently in [16][17][18][19][20][21]. We also show that at zeroth order in the derivative expansion, if one (i) takesh 1 to the horizon, i.e.…”

“…The complex conjugate on Ψ * UV [h 2 ,ḡ 2 ] is due to that the bulk manifold in the region between Σ 2 and ∂M 2 c has the opposite orientation from that between ∂M 1 c and Σ 1 . Connections between hydrodynamics and Schwinger-Keldysh contour have been made recently in various contexts in [14][15][16][17][18][19][20][21].…”

Effective actions for anomalous hydrodynamics

“…This framework was re-examined recently in [40] who suggested that it could be useful beyond the ideal fluid level; by studying the corrections to the ideal fluid effective action [41] argued that the transport of non-dissipative neutral fluids could be systematically understood in this framework. Moreover, this effective action approach has proven useful to understand aspects of anomalous transport in two dimensions [42], parity-odd Hall viscosity in three dimensions [43,44] and more recently even been argued to be useful in understanding aspects of dissipation [45][46][47].…”

Emergent supersymmetry in local equilibrium systems

“…The effective action I EFT incorporates dissipations and retardation effects from the bath of short-lived degrees of freedom (which have been integrated out) in a medium. Its general structure has recently been used to derive from first principle the local second law of thermodynamics [9], and a new formulation of fluctuating hydrodynamics has been proposed in terms of such an EFT [10,11] (see also [12][13][14][15][16][17]). See also [18] for a review of applications to driven open systems.…”