The scattering amplitude in simple quantum graphs is a well-known process which may be highly complex. In this work, motivated by the Shannon entropy, we propose a methodology that associates a graph with a scattering entropy, which we call the average scattering entropy. It is defined by taking into account the period of the scattering amplitude which we calculate using the Green's function procedure. We first describe the methodology on general grounds and then exemplify our findings considering several distinct groups of graphs. We go on and investigate other possibilities, one that contains groups of graphs with the same number of vertices, with the same degree, and the same number of edges, with the same length, but with distinct topologies and with different entropies. Another possibility we investigate contains graphs of the fishbone type, where the scattering entropy depends on the boundary conditions on the vertices of degree 1, with the corresponding values decreasing and saturating very rapidly as we increase the number of elementary structures in the graphs.

中文翻译：

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量子图的平均散射熵

简单量子图中的散射幅度是一个众所周知的过程，可能非常复杂。在这项工作中，受香农熵的启发，我们提出了一种将图与散射熵相关联的方法，我们称之为平均散射熵。它是通过考虑我们使用格林函数程序计算的散射幅度的周期来定义的。我们首先在一般情况下描述该方法，然后考虑几个不同的图组来举例说明我们的发现。我们继续研究其他可能性，其中包含具有相同顶点数、相同度数和相同边数、相同长度但具有不同拓扑和不同熵的图组。