几何热力学
Geometrothermodynamics
摘要：
我们介绍了几何热力学的基本原理，这是一种用微分几何概念研究热力学系统性质的方法。它一方面基于热力学相空间的熟知的接触结构，另一方面基于热力学平衡态空间的度规结构。为了使这两种结构相容，我们在相空间中引入一个勒让德不变的度量集，并要求它们的拉回产生平衡态空间上的度量。我们表明，Weinhold的度量，这是引入{ \it特设}，不包含在这个不变集。我们提出了替代度量，使我们能够重新定义的概念，热力学长度不变的方式和研究相变的曲率奇异性。
英文摘要：
We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the thermodynamic phase space and, on the other hand, on the metric structure of the space of thermodynamic equilibrium states. In order to make these two structures compatible we introduce a Legendre invariant set of metrics in the phase space, and demand that their pullback generates metrics on the space of equilibrium states. We show that Weinhold's metric, which was introduced {\it ad hoc}, is not contained within this invariant set. We propose alternative metrics which allow us to redefine the concept of thermodynamic length in an invariant manner and to study phase transitions in terms of curvature singularities.
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