内部能量,基本热力学关系,以及吉布斯集团理论作为统计计计数的新兴规律
1Department of Applied Mathematics, University of Washington, Seattle, WA 98195-3925, USA.
Entropy (Basel, Switzerland)
|January 8, 2025
概括
统计计数揭示了有限状态系统中的全息可观测值. Entropy Entropy
科学领域:
- 统计力学就是统计力学.
- 热力学是一种热力学.
- 信息理论是信息理论.
背景情况:
- 在有限状态系统中的统计计数可以被视为全息可观测.
- 论将经验频率与概率先验联系起来,当它们在大样本大小的极限上不同时.
研究的目的:
- 从统计计计数中推导出基本的热力学关系,而不依赖力学.
- 建立一个新的框架来理解内部能量及其与可观测的关系.
主要方法:
- 使用卡伦的定理和莱德-芬切尔变换.
- 应用统计动态与独立和相同分布的抽样.
- 分析在确定无限小的概率中的作用.
主要成果:
- 内部能量 (u) 作为实值可观的线性表示而出现.
- 吉布斯的基本热力学关系和集合理论是通过数学推导出来的.
- 在内部能量与其他热力学和分析量之间进行了新的类比.
结论:
- 内部能量可以被理解为从信息处理中产生的统计可观测值.
- 这种方法为热力学和统计力学提供了一个统一的数学框架.
- 这些发现为信息,能量和之间的关系提供了新的视角.
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