几何热力学中的二维Einstein流形
Two-dimensional Einstein manifolds in geometrothermodynamics
摘要：
我们提出了一类热力学系统的热力学曲率恒定，在热力学的几何方法的背景下，可以被解释为恒定的热力学相互作用的组件。特别是，对于由消失的海森曲率约束的系统，我们写下偏微分方程组。在这种情况下，有可能在由等温坐标的一阶导数构造的抽象空间中找到位于圆周上的解的子集。我们推测，解决方案的特征圆周是物理相关性，分离他们从那些纯粹的数学兴趣。我们提出的情况下，一个参数的家庭的基本关系-当躺在圆周-描述一个多变的流体。
英文摘要：
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In particular, for systems constrained by the vanishing of the Hessian curvature we write down the systems of partial differential equations. In such a case it is possible to find a subset of solutions lying on a circumference in an abstract space constructed from the first derivatives of the isothermal coordinates. We conjecture that solutions on the characteristic circumference are of physical relevance, separating them from those of pure mathematical interest. We present the case of a one-parameter family of fundamental relations that -- when lying in the circumference -- describe a polytropic fluid.
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