Lychagin Valentin, Roop Mikhail
V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Str., 117997 Moscow, Russia.
Faculty of Physics, Lomonosov Moscow State University, Leninskie Gory, 119991 Moscow, Russia.
Entropy (Basel). 2020 Oct 12;22(10):1147. doi: 10.3390/e22101147.
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.
我们展示了基于测量的热力学方法的发展。首先，我们回顾一下，将经典热力学视为广延变量的测量理论时，会将热力学状态描述为表示可测量量的平均值和极值测度的勒让德流形或拉格朗日流形。其次，随机向量的方差在相应的流形上诱导出黎曼结构。计算高阶中心矩时，会得到相应的高阶结构，即三次形式和四阶形式。三次形式决定了极值分布的偏度。其为零的条件给出了所谓的对称过程。四阶结构的正定性给热力学状态带来了额外的要求。
