Towards hydrodynamics without an entropy current

TL;DR

This paper introduces a generating functional approach to relativistic hydrodynamics that derives response constraints without relying on an entropy current, simplifying the computation of correlation functions.

Contribution

It presents a novel variational principle-based method that extends existing results and enables efficient calculation of hydrodynamic correlation functions.

Findings

Reproduces known hydrodynamic response results

Provides a new technique for computing n-point correlation functions

Eliminates the need for an entropy current in deriving constraints

Abstract

We present a generating functional which describes the equilibrium thermodynamic response of a relativistic system to external sources. A variational principle gives rise to constraints on the response parameters of relativistic hydrodynamics without making use of an entropy current. Our method reproduces and extends results available in the literature. It also provides a technique for efficiently computing n-point zero-frequency hydrodynamic correlation functions without the need to solve the equations of hydrodynamics.