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Stability analysis for a thermodynamically consistent model of relativistic fluid dynamics.

Laura Stricker1, Hans Christian Öttinger1

  • 1ETH Zürich, Department of Materials, Polymer Physics, CH-8093 Zurich, Switzerland.

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|February 21, 2019
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Summary

Relativistic fluid mechanics stability is enhanced using the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) framework. This approach ensures thermodynamic admissibility for relativistic hydrodynamics, distinguishing between liquids and gases.

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Area of Science:

  • Relativistic fluid mechanics
  • Non-equilibrium thermodynamics

Background:

  • Positive entropy production alone is insufficient for stability in relativistic fluid mechanics.
  • Advanced criteria for thermodynamic admissibility are crucial and available from non-equilibrium thermodynamics.

Purpose of the Study:

  • To perform a linear stability analysis of relativistic hydrodynamics using the GENERIC framework.
  • To investigate thermodynamic admissibility criteria for relativistic fluid models.

Main Methods:

  • Linear stability analysis applied to a relativistic hydrodynamics model.
  • Utilizing the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) framework.
  • Assuming a quadratic entropy function near thermodynamic equilibrium.

Main Results:

  • Stability is demonstrated for all physically meaningful parameters in relativistic fluid dynamics based on GENERIC.
  • The study reveals a fundamental distinction between liquids and gases in relativistic fluid dynamics through thermodynamic admissibility.

Conclusions:

  • The GENERIC framework provides robust stability for relativistic fluid dynamics.
  • Thermodynamic admissibility highlights inherent differences between relativistic liquids and gases.