AI 中文总结
该研究提出将信息内容（$C$）的方差作为统计复杂性度量，其满足相关准则，与热力学和相变直接关联，在二维伊辛模型等体系中验证了其特性，可捕捉关联系统的非平凡动力学结构。
AI 中文摘要
我们提出，信息论量信息内容（$C$）的方差可被自然地解释为统计复杂性的一种度量。我们证明$C$满足统计复杂性度量被广泛认可的准则：它在有序态和等概率态中均为零，而在中间区域达到最大值，且通常偏向有序方向。这一解释建立了与热力学及相变的直接联系：对于服从玻尔兹曼-吉布斯统计的系统，$C$是广延量，且与能量涨落、热容直接成正比。此外，不同于其他统计复杂性度量，$C$在连续相变处达到最大值，这一点在二维伊辛模型中得到了例证。对混沌映射和分数高斯噪声的应用进一步表明，$C$能捕捉不同类别的关联系统中的非平凡动力学结构。
英文摘要
We argue that the variance of the information content ($C$), an information-theoretic quantity, can be naturally interpreted as a measure of statistical complexity. We show that $C$ satisfies widely accepted criteria for statistical complexity measures: it vanishes for both ordered and equiprobable states, while attaining maxima in intermediate regimes, typically shifted toward order. This interpretation establishes direct connections with thermodynamics and phase transitions: for systems obeying Boltzmann--Gibbs statistics, $C$ is extensive and directly proportional to energy fluctuations and heat capacity. Moreover, unlike other statistical complexity measures, it attains a maximum at continuous phase transitions, as illustrated for the two-dimensional Ising model. Applications to chaotic maps and fractional Gaussian noise further indicate that $C$ captures nontrivial dynamical structure in different classes of correlated systems.
