两自由度非线性系统Weinhold度规的曲率
Curvature of the Weinhold metric for thermodynamical systems with 2 degrees of freedom
摘要：
本文研究了具有两个几何自由度系统的Weinhold（几何）度规的曲率。给出了高斯曲率$R$为零、正、负的条件。研究了Weinhold度规的特征变化和相边界处曲率的奇异性。详细讨论了具有常数$C_{v}$的系统的情况，包括理想气体和范德华气体，以及Berthelot气体的情况。
英文摘要：
In this work the curvature of Weinhold (thermodynamical) metric is studied in the case of systems with two thermodynamical degrees of freedom. Conditions for the Gauss curvature $R$ to be zero, positive or negative are worked out. Signature change of the Weinhold metric and the corresponding singular behavior of the curvature at the phase boundaries are studied. Cases of systems with the constant $C_{v}$, including Ideal and Van der Waals gases, and that of Berthelot gas are discussed in detail.
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