Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Effective field theory for dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current

Paolo Glorioso, Michael Crossley, Hong Liu

Abstract

In this paper we further develop the fluctuating hydrodynamics proposed in arXiv:1511.03646 in a number of ways. We first work out in detail the classical limit of the hydrodynamical action, which exhibits many simplifications. In particular, this enables a transparent formulation of the action in physical spacetime in the presence of arbitrary external fields. It also helps to clarify issues related to field redefinitions and frame choices. We then propose that the action is invariant under a $Z_2$ symmetry to which we refer as the dynamical KMS symmetry. The dynamical KMS symmetry is physically equivalent to the previously proposed local KMS condition in the classical limit, but is more convenient to implement and more general. It is applicable to any states in local equilibrium rather than just thermal density matrix perturbed by external background fields. Finally we elaborate the formulation for a conformal fluid, which contains some new features, and work out the explicit form of the entropy current to second order in derivatives for a neutral conformal fluid.

Effective field theory for dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current

Abstract

In this paper we further develop the fluctuating hydrodynamics proposed in arXiv:1511.03646 in a number of ways. We first work out in detail the classical limit of the hydrodynamical action, which exhibits many simplifications. In particular, this enables a transparent formulation of the action in physical spacetime in the presence of arbitrary external fields. It also helps to clarify issues related to field redefinitions and frame choices. We then propose that the action is invariant under a symmetry to which we refer as the dynamical KMS symmetry. The dynamical KMS symmetry is physically equivalent to the previously proposed local KMS condition in the classical limit, but is more convenient to implement and more general. It is applicable to any states in local equilibrium rather than just thermal density matrix perturbed by external background fields. Finally we elaborate the formulation for a conformal fluid, which contains some new features, and work out the explicit form of the entropy current to second order in derivatives for a neutral conformal fluid.

Paper Structure

This paper contains 32 sections, 226 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Action for fluctuating hydrodynamics
  3. Action in the fluid spacetime
  4. Formulation in physical spacetime
  5. Consequences of local KMS condition
  6. Classical limit
  7. Small $\hbar$ expansion
  8. Physical space formulation
  9. Dynamical KMS symmetry
  10. Proposal
  11. The classical limit
  12. Open issues at finite $\hbar$
  13. Dynamical KMS invariance and entropy current
  14. Dynamical KMS invariance
  15. Explicit tensor analysis to first order in derivative expansion
  16. ...and 17 more sections

Figures (1)

  • Figure 1: Relations between the fluid spacetime and two copies of physical spacetimes. The red straight line in the fluid spacetime with constant $\sigma^i$ is mapped by $X^\mu_{1,2} (\sigma^0, \sigma^i)$ to physical spacetime trajectories (also in red) of the corresponding fluid element.