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Metriplectic four-bracket algorithm for constructing thermodynamically consistent dynamical systems.

Azeddine Zaidni1, Philip J Morrison2

  • 1Mohammed VI Polytechnic University, College of Computing, Lot 660, Hay Moulay Rachid, Ben Guerir 43150, Morocco.

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Summary
This summary is machine-generated.

A novel unified thermodynamic algorithm constructs consistent dynamical systems, conserving energy while generating entropy. This approach, based on the metriplectic 4-bracket, generalizes key fluid dynamics and thermodynamics models.

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Area of Science:

  • Thermodynamics
  • Fluid Dynamics
  • Mathematical Physics

Background:

  • Dynamical systems require thermodynamic consistency, balancing energy conservation with entropy production.
  • Existing models often lack a unified framework for Hamiltonian and dissipative dynamics.

Purpose of the Study:

  • To present a unified thermodynamic algorithm for constructing thermodynamically consistent dynamical systems.
  • To generalize existing fluid dynamics and thermodynamics models.

Main Methods:

  • The algorithm is based on the metriplectic 4-bracket formulation.
  • It incorporates a force-flux relation: J^{α}=-L^{αβ}∇(δH/δξ^{β}).
  • The method is applied to Navier-Stokes-Fourier, Cahn-Hilliard-Navier-Stokes, and Brenner-Navier-Stokes-Fourier systems.

Main Results:

  • The unified algorithm successfully constructs thermodynamically consistent dynamical systems.
  • Significant generalizations of the Navier-Stokes-Fourier, Cahn-Hilliard-Navier-Stokes, and Brenner-Navier-Stokes-Fourier systems were achieved.
  • The force-flux relation provides a clear link between phenomenological coefficients, Hamiltonian, and dynamical variables.

Conclusions:

  • The presented algorithm offers a unified approach to modeling complex thermodynamic systems.
  • This framework enhances the consistency and applicability of fluid dynamics and thermodynamics models.
  • The generalization of established systems opens new avenues for research in nonequilibrium thermodynamics.