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The Conservation-Dissipation Formalism (CDF) offers a robust framework for developing stable models of irreversible processes. This review highlights its mathematical foundations and diverse applications in physics and beyond.

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conservation–dissipation formalismhyperbolic PDEsnon-equilibrium thermodynamicssoft matter physicsviscoelastic fluids

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Area of Science:

  • Thermodynamics
  • Mathematical Physics
  • Non-equilibrium Systems

Background:

  • Irreversible processes require models that are both thermodynamically consistent and mathematically stable.
  • Existing models may face challenges in ensuring well-posedness for complex systems.

Purpose of the Study:

  • To review recent advancements in the Conservation-Dissipation Formalism (CDF).
  • To explore the physical motivations and mathematical underpinnings of CDF.
  • To showcase its applications across various scientific disciplines.

Main Methods:

  • Summarizing the theoretical framework of CDF.
  • Reformulating classical models (e.g., Fokker-Planck, Boltzmann equations) using CDF.
  • Examining connections with other non-equilibrium thermodynamics theories.

Main Results:

  • CDF provides a unified approach for constructing stable and thermodynamically compatible models.
  • Demonstrated successful application of CDF to diverse phenomena like non-Fourier heat conduction and viscoelastic fluids.
  • Established links between CDF and established theories in non-equilibrium thermodynamics.

Conclusions:

  • The Conservation-Dissipation Formalism presents a powerful and versatile tool for modeling irreversible processes.
  • CDF facilitates the development of accurate and stable models with broad applicability.
  • Further research is encouraged to explore novel applications of CDF.