Considering a large class of muscle contraction models accounting for actin–myosin interaction, we present a mathematical setting in which solution properties can be established, including fundamental thermodynamic balances. Moreover, we propose a complete discretization strategy for which we are also able to obtain discrete versions of the thermodynamic balances and other properties. Our major objective is to show how the thermodynamics of such models can be tracked after discretization, including when they are coupled to a macroscopic muscle formulation in the realm of continuum mechanics. Our approach allows to carefully identify the sources of energy and entropy in the system, and to follow them up to the numerical applications.

中文翻译：

---

肌肉收缩模型的热力学性质和相关的离散时间原理

考虑到考虑肌动蛋白-肌球蛋白相互作用的一大类肌肉收缩模型，我们提出了一个数学设置，可以在其中建立溶液特性，包括基本的热力学平衡。此外，我们提出了一个完整的离散化策略，为此，我们还可以获得热力学天平和其他属性的离散版本。我们的主要目标是展示离散化后如何跟踪此类模型的热力学，包括将它们与连续体力学领域中的宏观肌肉公式耦合时的情况。我们的方法允许仔细地识别系统中的能量和熵的来源，并将其遵循数值应用。