Non-statistical thermodynamic optimization

CALPHAD方法用于通过同时处理关于相和多相混合物的热力学性质以及相平衡条件的实验数据来构造相的热力学模型。尽管有热力学的味道，该方法实际上是一个非线性最小二乘技术，导致在统计上最优的向量模型的参数沿着与他们的协方差矩阵。对所得解的分析要求输入数据具有一定的统计特性。特别是，有必要为每一次测量确定一个合理的实验误差，并确保其内涵符合数理统计中采用的内涵。在现实中，对实验误差的艰苦分析往往被他们的估计所取代，这些估计反映了提出这些估计的专家的个人意见和经验。与其猜测这种普遍的做法是好是坏，让我们认识到它剥夺了“实验误差”的统计意义。还应该注意到，在许多当代出版物中，观察的准确性没有得到重视，实验数据表越来越频繁地被可视化这些数据的数字所取代。扫描和数字化这些插图并不是问题;问题是扫描和数字化导致统计上无意义的数量。它并不打算开始一场无望的斗争，反对今天传播实验知识的一种应受谴责的方式。人们设想通过一种新的评估技术来增强CALPHAD方法，该技术基于Leonid V. Kantorovich制定的实验信息的非统计处理的思想和算法，并成功地用于解决经济问题。新的过程将产生的不是模型的参数向量，但它们的值的区域（不一定是凸的），在其中可以尝试满足额外的标准，如不存在反转的可扩展性差距或沿着相边界的假拐点。对于该区域的任何点，它保证反算的量被限制在与所有实验观测相关的“最终误差”的非统计走廊内。

CALPHAD method is used for constructing thermodynamic models of phases via a simultaneous treatment of experimental data on the thermodynamic properties of phases and multiphase mixtures, and on the conditions of phase equilibria. Despite a thermodynamic flavour, the method is in fact a non-linear least squares technique resulting in a statistically optimal vector of models' parameters along with their covariance matrix. An analysis of the solution obtained requires that input data possess certain statistical characteristics. In particular, it is necessary to ascribe a reasonable experimental error to each measurement, and to ensure that its connotation conforms to that adopted in mathematical statistics. In reality, a painstaking analysis of experimental errors is often replaced with their estimations reflecting a personal opinion and experience of an expert proposing these estimations. Instead of speculating whether this widespread practice is good or bad, let us realize that it strips the "experimental errors" of their statistical meaning. It should also be noticed that in many contemporary publications, an accuracy of observations is not paid attention, that tables of experimental data are more and more frequently replaced with figures visualizing these data. It is not a problem to scan and digitize these illustrations; the problem is that scanning and digitizing lead to statistically meaningless quantities. It is not intended to commence a hopeless struggle against a reproachable way in which experimental knowledge is disseminated today. It is contemplated to augment the CALPHAD method by a new assessment technique based on the ideas and algorithms of a non-statistical treatment of experimental information formulated by Leonid V. Kantorovich and successfully employed for solving economic problems. The new procedure will yield not the vector of models' parameters, but a region (not necessarily convex) of their values within which one can try to satisfy additional criteria such as an absence of inverted miscibility gaps or false inflection points along phase boundaries. For any point from this region, it guaranteed that back-calculated quantities are confined within a non-statistical corridor of "ultimate errors" associated with all experimental observations.