提出新型信息流建模方法，可捕捉周期性反馈机制。
Generalized Derangetropy Functionals for Modeling Cyclical Information Flow
- 用非线性微分方程定义熵调制变换，直接作用于概率密度。
- 递归应用后信息演化趋近高斯特征函数，具收敛性定理支撑。
- 适合研究带周期结构与反馈的神经网络、通信系统等场景。
本文提出一种广义的熵调制变换框架——去排列熵泛函，用于建模循环与反馈驱动的信息流。不同于静态的香农熵等标量度量，该泛函直接作用于概率密度，提供分布支撑上的信息结构拓扑表征。框架能捕捉信息分布的周期性与自指特性，并通过由非线性微分方程控制的算子实现编码。当递归应用时，这些算子诱导出由热方程支配的谱扩散过程，最终收敛至高斯特征函数。该收敛定理为周期调制下信息长期动态提供了统一分析基础。新框架可用于分析具有周期结构、随机反馈和延迟交互的系统中信息的时序演化，适用于人工神经网络、通信理论与非平衡统计力学等领域。
原文摘要 · Abstract (English)
This paper introduces a framework for modeling cyclical and feedback-driven information flow through a generalized family of entropy-modulated transformations called derangetropy functionals. Unlike scalar and static entropy measures such as Shannon entropy, these functionals act directly on probability densities and provide a topographical representation of information structure across the support of the distribution. The framework captures periodic and self-referential aspects of information distribution and encodes them through functional operators governed by nonlinear differential equations. When applied recursively, these operators induce a spectral diffusion process governed by the heat equation, leading to convergence toward a Gaussian characteristic function. This convergence theorem provides a unified analytical foundation for describing the long-term dynamics of information under cyclic modulation. The proposed framework offers new tools for analyzing the temporal evolution of information in systems characterized by periodic structure, stochastic feedback, and delayed interaction, with applications in artificial neural networks, communication theory, and non-equilibrium statistical mechanics.
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