Michos Ioannis, Raptis Vasilios
Department of Computer Science and Engineering, School of Sciences, European University Cyprus, 6 Diogenous Str., Nicosia 2404, Cyprus.
Institute of Nanoscience and Nanotechnology, National Scientific Research Center 'Demokritos', Patr. Gregoriou E & 27 Neapoleos, 15341 Agia Paraskevi, Greece.
Entropy (Basel). 2023 Oct 31;25(11):1504. doi: 10.3390/e25111504.
We study partitions (equitable, externally equitable, or other) of graphs that describe physico-chemical systems at the atomic or molecular level; provide examples that show how these partitions are intimately related with symmetries of the systems; and discuss how such a link can further lead to insightful relations with the systems' physical and chemical properties. We define a particular kind of graph partition, which we call Chemical Equitable Partition (CEP), accounting for chemical composition as well as connectivity and associate it with a quantitative measure of information reduction that accompanies its derivation. These concepts are applied to model molecular and crystalline solid systems, illustrating their potential as a means to classify atoms according to their chemical or crystallographic role. We also cluster materials in meaningful manners that take their microstructure into account and even correlate them with the materials' physical properties.
我们研究用于描述原子或分子水平上物理化学系统的图的划分（公平划分、外部公平划分或其他划分）；给出示例说明这些划分如何与系统的对称性密切相关；并讨论这种联系如何进一步导致与系统物理和化学性质的深刻关系。我们定义了一种特殊的图划分，称之为化学公平划分（CEP），它既考虑了化学成分，又考虑了连通性，并将其与推导过程中伴随的信息减少的定量度量相关联。这些概念被应用于对分子和晶体固体系统进行建模，展示了它们作为根据原子的化学或晶体学作用对原子进行分类的一种手段的潜力。我们还以有意义的方式对材料进行聚类，同时考虑它们的微观结构，甚至将它们与材料的物理性质相关联。
