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Effective field theory of dissipative fluids. II: Classical limit, dynamical KMS symmetry and entropy current. (English) Zbl 1382.81205
Summary: In this paper we further develop the fluctuating hydrodynamics proposed in our Paper I [ibid. 2017, No. 9, Paper No. 95, 82 p. (2017; Zbl 1382.81199)] 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.

MSC:
81T60 Supersymmetric field theories in quantum mechanics
82B10 Quantum equilibrium statistical mechanics (general)
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
94A17 Measures of information, entropy
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