In this talk I will present our recently-developed Conservation-Dissipation Formalism (CDF) of non-equilibrium thermodynamics. The formalism is based on a stability criterion, which was proposed after observing many existing PDE models. With this formalism, we formulate novel thermodynamics theories for heat conduction in rigid bodies and non-isothermal compressible Maxwell fluid flows. I will also show that the constructed PDEs meet four fundamental requirements: the robustness, irreversibility, long-time tendency to equilibrium, and compatibility with the possibly existing classical models.

 

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