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This study introduces a new framework for relativistic fluctuating hydrodynamics, ensuring causal and stable theories. It uses a covariant fluctuation theorem to constrain out-of-equilibrium dynamics and establish fluctuation-dissipation relations.

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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.