关于热力学第三定律的注记。I
Notes on the Third Law of Thermodynamics.I
摘要：
我们分析了热力学第三定律的某些方面。我们首先回顾熵的版本（N）和不可达性版本（U）和它们之间发生的关系。然后，我们解释（N）作为一个连续性边界条件的热力学边界T=0的热力学域。在严格的数学基础上，我们讨论了第三定律都在Carathéodory的方法和吉布斯的一个。Carathéodory的方法是基本的，以了解表面的性质T=0。事实上，在这种方法中，在适当的数学条件下，T=0表现为与非奇异可积Pfiran形式$δQ_{rev}$相关联的热力学流形的叶理的一片叶子。作为一片叶，它不能与叶理的任何其他叶$S=$相交。我们证明了（N）等价于T=0是叶的要求。在吉布斯的方法中，T=0的特殊性质似乎不那么明显，因为熵的存在是一个假设;然而，仍然可以得出结论，熵的最低值必须属于定义函数的凸集的边界。
英文摘要：
We analyze some aspects of the third law of thermodynamics. We first review both the entropic version (N) and the unattainability version (U) and the relation occurring between them. Then, we heuristically interpret (N) as a continuity boundary condition for thermodynamics at the boundary T=0 of the thermodynamic domain. On a rigorous mathematical footing, we discuss the third law both in Carathéodory's approach and in Gibbs' one. Carathéodory's approach is fundamental in order to understand the nature of the surface T=0. In fact, in this approach, under suitable mathematical conditions, T=0 appears as a leaf of the foliation of the thermodynamic manifold associated with the non-singular integrable Pfaffian form $δQ_{rev}$. Being a leaf, it cannot intersect any other leaf $S=$ const. of the foliation. We show that (N) is equivalent to the requirement that T=0 is a leaf. In Gibbs' approach, the peculiar nature of T=0 appears to be less evident because the existence of the entropy is a postulate; nevertheless, it is still possible to conclude that the lowest value of the entropy has to belong to the boundary of the convex set where the function is defined.
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