Effective Action for Relativistic Hydrodynamics from the Crooks Fluctuation Theorem

Area of Science:

• Theoretical Physics
• Statistical Mechanics
• General Relativity

Background:

• Fluctuating hydrodynamics describes fluid behavior with fluctuations.
• Relativistic regimes require advanced theoretical frameworks.
• Ensuring causality and stability in effective theories is crucial.

Purpose of the Study:

• To derive a new effective theory framework for fluctuating hydrodynamics in the relativistic regime.
• To establish conditions for causality, stability, and well-posedness within general relativity.
• To investigate the role of out-of-equilibrium fluctuations and their constraints.

Main Methods:

• Utilizing standard thermodynamical principles.
• Applying general properties of nonequilibrium stochastic dynamics.
• Developing a relativistically covariant version of the Crooks fluctuation theorem.

Main Results:

• A new effective theory framework for relativistic fluctuating hydrodynamics.
• Clear conditions for ensuring causal, stable, and well-posed effective theories.
• Emerging Z_{2} symmetry imposing fluctuation-dissipation relations for n-point correlation functions.

Conclusions:

• The derived framework is valid in the full nonlinear regime and independent of spacetime foliation.
• The covariant fluctuation theorem constrains entropy production in driven systems.
• The results align with standard constraints for the Schwinger-Keldysh effective action.