内在信息 - 理论模型
1Department of Genetics, Microbiology and Statistics, Faculty of Biology, Universitat de Barcelona, 08028 Barcelona, Spain.
Entropy (Basel, Switzerland)
|May 24, 2024
概括
这项研究开发了一个信息几何框架用于物理学,将信息源建模为多变量正常分布. 结果显示不变,内在模型对于量子物理基础至关重要.
科学领域:
- 数学物理 数学物理
- 信息几何学信息几何学
- 量子物理基础 量子物理基础
背景情况:
- 之前的工作为物理对象建立了一个信息几何框架.
- 本文通过放宽信息来源的独立性条件来扩大框架.
研究的目的:
- 开发一个基于信息几何学的数学框架来表示物理对象.
- 为物理学,特别是量子物理学奠定信息基础.
- 探索放松独立条件对信息建模的影响.
主要方法:
- 使用单变量和多变量正常概率分布建模信息源.
- 应用信息几何学和量子力学 (施罗丁格方程) 的概念.
- 使用马哈拉诺比斯距离和克拉梅尔-拉奥下界.
主要成果:
- 松散的独立性导致将信息建模为具有多变量正常分布的模式.
- 信息被分解成量子波器,产生内在的能量水平.
- 预期的二次马哈拉诺比斯距离等于量子波器能量水平.
- 全球概率密度函数与贝叶斯后面分布与之前的里曼体积相匹配.
结论:
- 扩展框架引入了复杂性,但产生了不变的,内在的信息理论模型.
- 这些内在模型对于建立物理学基础原则至关重要.
- 这项研究加强了信息几何学,量子力学和统计推理之间的联系.
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