发表机构
Dzhelepov Laboratory of Nuclear Problems, JINR; Dubna State University; Meshcheryakov Laboratory of Information Technologies, JINR; HSE University（杜布纳联合核子问题实验室; 杜布纳国立大学; 杜布纳联合信息技术研究实验室; 高等经济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为二维Thomson问题建立基于Shannon熵的信息论框架，证明熵平衡律与拓扑荷求和规则，并揭示边界熵饱和条件，数值验证了成核、无序峰值及边界饱和尺度。
AI 中文摘要
我们基于Voronoi拓扑荷分布的Shannon熵，为硬壁圆盘上二维Thomson问题的已知最小能量构型建立了一个完整的信息论框架。两个精确结果被证明，并对所有研究的系统尺寸$N=12$--$10^5$成立。首先，一个熵平衡律将总熵无近似地分解为体相、边界和混合贡献。其次，一个拓扑荷求和规则将总荷固定为边界粒子数的两倍加六；结合观察到的体相与边界配位数的分离，它给出了三配位和四配位边界粒子数目与体相荷之间的精确关系。我们进一步证明边界熵受二元最大值约束，且该约束的饱和等价于每个边界粒子的体相荷趋近负二分之一，这一机制本身将框架限制为至少十二个粒子的边界。所有恒等式均以机器精度数值验证，定位体相成核于56个粒子，全局无序度最大值于146，以及边界饱和的起始于约1000以上。该框架可推广到闭合球面几何，其中总荷固定为十二。
英文摘要
We establish a complete information-theoretic framework for the known minimum-energy configurations of the two-dimensional Thomson problem on a hard-wall disk, based on the Shannon entropy of the Voronoi topological charge distribution. Two exact results are proven and hold for all studied systems of size $N=12$-$10^5$. First, an entropy balance law decomposes the total entropy into bulk, boundary, and mixing contributions without approximation. Second, a topological charge sum rule fixes the total charge at twice the number of boundary particles plus six; together with the observed separation of bulk and boundary coordination numbers, it yields exact relations between the populations of three- and four-coordinated boundary particles and the bulk charge. We further prove that the boundary entropy is bounded by the binary maximum and that saturation of this bound is equivalent to the bulk charge per boundary particle approaching minus one half, a regime that the framework itself restricts to boundaries of at least twelve particles. All identities are verified numerically to machine precision, locating bulk nucleation at $56$ particles, the maximum of global disorder at $146$, and the onset of boundary saturation beyond about $1000$. The framework carries over to closed spherical geometry, where the total charge is fixed at twelve.
CommentsArticle: 21 pages, 2 figures; Supplemental material: 12 pages, 1 table
