Conservation-dissipation formalism of irreversible thermodynamics

Yi Zhu Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China Liu Hong Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China Zaibao Yang Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China Wen-An Yong Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China

Analysis of PDEs mathscidoc:2204.03011

Journal of Non-Equilibrium Thermodynamics, 40, (2), 67-74, 2015.5
We propose a conservation-dissipation formalism (CDF) for coarse-grained descriptions of irreversible processes. This formalism is based on a stability criterion for non-equilibrium thermodynamics. The criterion ensures that non-equilibrium states tend to equilibrium in long time. As a systematic methodology, CDF provides a feasible procedure in choosing non-equilibrium state variables and determining their evolution equations. The equations derived in CDF have a unified elegant form. They are globally hyperbolic, allow a convenient definition of weak solutions, and are amenable to existing numerics. More importantly, CDF is a genuinely nonlinear formalism and works for systems far away from equilibrium. With this formalism, we formulate novel thermodynamics theories for heat conduction in rigid bodies and non-isothermal compressible Maxwell fluid flows as two typical examples. In these examples, the non-equilibrium variables are exactly the conjugate variables of the heat fluxes or stress tensors. The new theory generalizes Cattaneo’s law or Maxwell’s law in a regularized and nonlinear fashion.
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@inproceedings{yi2015conservation-dissipation,
  title={Conservation-dissipation formalism of irreversible thermodynamics},
  author={Yi Zhu, Liu Hong, Zaibao Yang, and Wen-An Yong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428152917433501152},
  booktitle={Journal of Non-Equilibrium Thermodynamics},
  volume={40},
  number={2},
  pages={67-74},
  year={2015},
}
Yi Zhu, Liu Hong, Zaibao Yang, and Wen-An Yong. Conservation-dissipation formalism of irreversible thermodynamics. 2015. Vol. 40. In Journal of Non-Equilibrium Thermodynamics. pp.67-74. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428152917433501152.
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