对非平衡离散系统的概括集体理论的矩阵方法
1Chinese Academy of Military Science, Chinese Academy of Military Science, Defense Innovation Institute, Beijing 100071, China and Intelligent Game and Decision Laboratory, Beijing 100071, China.
Physical review. E
|January 21, 2026
概括
研究人员开发了一个基于矩阵的框架,用于在离散不平衡系统中通用集体理论. 这种方法统一了概率分布和热力学关系,为复杂系统分析提供了新的途径.
科学领域:
- 统计力学 统计力学
- 理论物理 理论物理
- 复杂的系统复杂的系统.
背景情况:
- 目前还没有针对不平衡系统的通用框架.
- 现有的理论很难严格地解决离散的不平衡系统.
- 有需要一个统一的方法来概括集团理论.
研究的目的:
- 为离散不平衡系统的通用集合理论提供简洁而严格的框架.
- 建立适用于各种离散系统的基于矩阵的方法.
- 统一对不平衡环境中的概率分布和热力学关系的理解.
主要方法:
- 开发一种基于矩阵的方法,用于通用集体理论.
- 引入观察矩阵来制定通用博尔兹曼分布.
- 确定用于推断博尔兹曼分布的最小足够的统计数据.
主要成果:
- 任何离散的概率分布都可以用一般化的博尔兹曼分布来表述.
- 可以观察到的物质及其并联变量作为基向量和坐标.
- 没有平衡的热力学和波动分散关系自然地从框架中出现.
结论:
- 拟议的基于矩阵的框架为离散不平衡系统的概括集合理论提供了一种通用和严格的方法.
- 这项工作为分析复杂系统及其新出现的特性提供了新的视角.
- 这些发现为开发非平衡统计力学高级理论工具铺平了道路.
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