混沌放松过程的热力学
1School of Mathematical Sciences, <a href="https://ror.org/03jc41j30">Jiangsu University</a>, Zhenjiang 212013, China.
Physical review. E
|September 19, 2024
概括
这项研究将热力学形式主义扩展到非平衡的混乱系统,将信息和逃脱率与可观测的平均值联系起来. 新的理论使用转移运算符的自函数预测可观测的相空间概况.
科学领域:
- 热力学是一种热力学.
- 非平衡的统计力学.
- 混沌理论是一个混乱理论.
背景情况:
- 已建立的热力学形式主义适用于处于统计平衡状态的系统.
- 许多复杂系统在达到稳定状态之前存在于非平衡状态.
研究的目的:
- 将热力学形式主义概括为平衡状态之外的非平衡系统.
- 建立信息,逃逸率和可观测的平均值之间的有限时间关系.
- 开发一种方法来预测可观测的相位空间概况.
主要方法:
- 热力学形式主义对混乱动力学的概括.
- 导出信息,逃逸率和相空间平均值之间的关系.
- 使用Peron-Frobenius或Koopman转移运算符的领先和子领先特有函数.
主要成果:
- 对于非平衡混乱系统的有限时间动态的概括热力学形式主义.
- 集成可观测的相空间概况的预测框架.
- 在基准混乱地图上进行分析和数值验证 (伯努利,扰乱猫,亨农,伊凯达).
结论:
- 开发的理论准确地描述了非平衡的混乱动态.
- 转移运算子自函数提供了对可观测分布的关键见解.
- 这种方法为分析超出平衡的复杂系统提供了一个强大的工具.
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