Effective action for relativistic hydrodynamics from Crooks fluctuation theorem

TL;DR

This paper develops a relativistic fluctuating hydrodynamics framework ensuring causality, stability, and well-posedness, using thermodynamics and Crooks fluctuation theorem to constrain out-of-equilibrium fluctuations and derive fluctuation-dissipation relations.

Contribution

It introduces a novel effective theory for relativistic hydrodynamics based on thermodynamics and fluctuation theorems, ensuring key physical properties are maintained in the nonlinear regime.

Findings

Established conditions for causality and stability in relativistic hydrodynamics

Derived a covariant Crooks fluctuation theorem for out-of-equilibrium fluctuations

Identified a $ ext{Z}_2$ symmetry leading to fluctuation-dissipation relations

Abstract

A new effective theory framework for fluctuating hydrodynamics in the relativistic regime is derived using standard thermodynamical principles and general properties of non-equilibrium stochastic dynamics. For the first time, we establish clear and concise conditions for ensuring that the resulting effective theories are causal, stable, and well-posed within general relativity. These properties are independent of spacetime foliation and are valid in the full nonlinear regime. Out-of-equilibrium fluctuations are constrained by a relativistically covariant version of Crooks fluctuation theorem, which determines how the entropy production is distributed even when the system is driven by an external force. This leads to an emerging $\mathbb{Z}_2$ symmetry responsible for imposing fluctuation-dissipation relations for n-point correlation functions, which matches the standard constraints for the Schwinger-Keldysh effective action.