Abstract In the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

中文翻译：

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由一个扩展势函数公式化的内变量理论

摘要 在内部变量的动力学速率定律中，通常假设内部变量的速率取决于内部变量和状态变量的共轭力。对共轭力的依赖已经围绕流势函数得到了充分的解决。动力学速率定律可以用两个势函数来表述，自由能函数和流动势函数。对状态变量的依赖还没有得到很好的解决。受 JR Rice 先前对内变量理论的渐近稳定性研究的启发，本文讨论了对状态变量的依赖性的热力学意义。本文表明，如果内部变量的速率不明确依赖于内部变量，则动力学速率定律可以通过在扩展状态空间中定义的一个扩展势函数来表述。扩展状态空间由状态变量和内部变量的比率跨越。此外，如果内部变量的比率不明确依赖于状态变量，则可以基于扩展势函数建立扩展吉布斯方程，从中可以恢复所有本构方程。这项工作可以被认为是内变量理论的某种拉格朗日公式。如果内部变量的比率不明确依赖于状态变量，则可以基于扩展势函数建立扩展吉布斯方程，从中可以恢复所有本构方程。这项工作可以被认为是内变量理论的某种拉格朗日公式。如果内部变量的比率不明确依赖于状态变量，则可以基于扩展势函数建立扩展吉布斯方程，从中可以恢复所有本构方程。这项工作可以被认为是内变量理论的某种拉格朗日公式。