We introduce a family of scale-invariant entropy statistics derived from logarithmically aggregated distance distributions of point processes, with prime numbers serving as a motivating example. The construction associates to each finite configuration a scalar quantity encoding structural features of relative spacing while remaining insensitive to absolute scale. This work is intended as a methodological contribution rather than a source of new raw results.

翻译：我们提出了一族从点过程距离分布的对数聚合中导出的尺度不变熵统计量，其中素数分布作为启发性示例。该构造将每个有限构型与一个标量量相关联，该标量量编码相对间隔的结构特征，同时保持对绝对尺度的不敏感性。本工作旨在作为方法论贡献，而非新原始结果的来源。