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arXiv · 2501.04637

Effective action for relativistic hydrodynamics from Crooks fluctuation theorem

Nicki Mullins·Mauricio Hippert·Jorge Noronha
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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.

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Nicki Mullins, Mauricio Hippert, Jorge Noronha. 2025-01-08. Effective action for relativistic hydrodynamics from Crooks fluctuation theorem. https://arxiv.org/abs/2501.04637

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