Shannon information entropy of fractional occupation probability as an electron correlation measure in atoms and molecules

Local Entanglement of Electrons in 1D Hydrogen Molecule

The quantum entanglement entropy of the electrons in a one-dimensional hydrogen molecule is quantified locally using an appropriate partitioning of the two-dimensional configuration space. Both the global and the local entanglement entropy exhibit a monotonic increase when increasing the inter-nuclear distance, while the local entropy remains peaked in the middle between the nuclei with its width decreasing. Our findings show that at the inter-nuclear distance where a stable hydrogen molecule is formed, the quantum entropy shows no peculiarity thus indicating that the entropy and the energy measures display different sensitivity with respect to the interaction between the two identical electrons involved. One possible explanation is that the calculation of the quantum entropy does not account explicitly for the distance between the nuclei, which contrasts to the total energy calculation where the energy minimum depends decisively on that distance. The numerically exact and the time-dependent quantum Monte Carlo calculations show close results.

Information Entropy in Chemistry: An Overview

Basic applications of the information entropy concept to chemical objects are reviewed. These applications deal with quantifying chemical and electronic structures of molecules, signal processing, structural studies on crystals, and molecular ensembles. Recent advances in the mentioned areas make information entropy a central concept in interdisciplinary studies on digitalizing chemical reactions, chemico-information synthesis, crystal engineering, as well as digitally rethinking basic notions of structural chemistry in terms of informatics.

Complex network dynamics of the topological structure in a geochemical field from the Nanling area in South China

The topological classification of geochemical elements is widely used as a reference for regional prospecting prediction. In this study, we analyze the topological correlation structures of 39 representative geochemical elements from the Nanling area of South China by implementing the complex networks theory. The topological correlation structures of geochemical elements have a high clustering coefficient (0.8120–0.8880), but the magnitude of the shortest path (1.2950–2.3600) is small. In combination with the analysis of complex networks characteristics, we report that the topological correlation structures of the geochemical elements in this area have small-world characteristics, which reveals the self-organized criticality. As shown in the topological network, two random elements have some level of associations, which present a specific community feature. Our preliminary result shows that with changing the control parameter (k) of “coarse-graining”, the topological correlation structures undergo two critical phase transitions. As the control parameter (k) reaches 0.44, the entire element system evolves into two parts. When the control parameter (k) reaches 0.63, the system forms three “communities”. It is worth noting that the three “communities” are basically consistent with the Goldschmidt’s geochemical classification of the elements, which are lithophile, siderophile, and chalcophile groups, respectively. In these “communities”, we also found that a small level of component units is nested.

Optimal Flow Distribution of Military Supply Transportation Based on Network Analysis and Entropy Measurement

One important element of military supply transportation is concealment, especially during war preparations and warfare periods. By introducing entropy to calculate the transportation concealment degree, we investigate the issue about concealed military supply transportation on the whole road network and propose an optimal flow distribution model. This model's objective function is to maximize the concealment of military supply transportation. After analyzing the road network, classifying different nodes, summarizing the constraint conditions based on the properties and assumptions in the transportation process, and combining the general parameter limits, the optimal flow distribution model is further transformed into a calculable non-linear programming model. Thus, based on this non-linear programming model, we can obtain the optimal distribution scheme of military supply transportation from the perspectives of network analysis and concealment measurement. Lastly, an example of military supply transportation in Jiangsu province, China is illustrated to prove the feasibility of the proposed model. The managerial implication is that by utilizing the proposed flow distribution model, military supplies can be efficiently transported to the required destinations based on maximizing the concealment degree. Not only this model can be utilized in the real military supply transportation, it can be also applied in other transportation fields which require time efficiency and concealment.

Controlling the shannon entropy of quantum systems

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.