论文标题
在热力学的高阶结构上
On Higher Order Structures in Thermodynamics
论文作者
论文摘要
我们介绍了基于测量的热力学方法的发展。首先，我们回想起，将经典热力学视为对广泛变量的测量理论，人们将热力学状态描述为代表可测量数量和极端措施的平均值的传奇人物或拉格朗日歧管。其次，随机矢量的方差在相应的歧管上诱导Riemannian结构。计算高阶中央力矩，一个人驱动到相应的高阶结构，即立方和第四阶形成。立方形式负责极端分布的偏度。其零的条件为我们提供了所谓的对称过程。第四阶结构的积极性为我们提供了热力学状态的额外要求。
We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic states as Legendrian or Lagrangian manifolds representing the average of measurable quantities and extremal measures. Secondly, the variance of random vectors induces the Riemannian structures on the corresponding manifolds. Computing higher order central moments one drives to the corresponding higher order structures, namely, the cubic and the fourth order forms. The cubic form is responsible for the skewness of the extremal distribution. The condition for it to be zero gives us so-called symmetric processes. The positivity of the fourth order structure gives us an additional requirement to thermodynamic state.
