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

## TL;DR

This paper advances the theoretical framework of fluctuating hydrodynamics by detailing the classical limit, introducing a new dynamical KMS symmetry, and deriving the entropy current for conformal fluids, enhancing understanding of dissipative fluid dynamics.

## Contribution

It introduces a classical limit formulation of hydrodynamical action, proposes a dynamical KMS symmetry, and derives the entropy current for conformal fluids, broadening the theoretical tools for dissipative fluid analysis.

## Key findings

- Classical limit simplifies the hydrodynamical action.
- Dynamical KMS symmetry generalizes local KMS condition.
- Explicit entropy current for conformal fluids to second order.

## 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.