关于一般相对论中的热力学克鲁伯格理论
Francesco Farsaci1, Patrizia Rogolino1
1Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d'Alcontres, 31, 98166 Messina, Italy.
Entropy (Basel, Switzerland)
|August 28, 2025
概括
这项研究扩展了非平衡热力学,使用里曼空间内的内部变量,与广义相对论保持一致. 它提出了热力学第二定律,并为不弹性和粘性应力推导了关键张量.
科学领域:
- 热力学
- 一般相对论
- 微分几何学
背景情况:
- 具有内部变量的非平衡热力学需要一个与广义相对论相容的框架.
- 现有的配方可能无法完全整合里曼的几何和热力学原理.
研究的目的:
- 用里曼空间中的内部变量来制定非平衡热力学.
- 在这个几何背景下概括热力学第二定律.
- 导出密度,不弹性和粘性应力张量以及产量的表达式.
主要方法:
- 使用克鲁伯格的非平衡热力学公式.
- 应用热力学第二定律在一般坐标与伪欧几里德度量.
- 在里曼空间中推导出类似Levi-Civita的能量张量和密度.
主要成果:
- 一个与托尔曼的方法一致的热力学第二定律被提出.
- 确定了密度,不弹性和粘性应力张量以及产量的表达式.
- 导出的表达式遵循一般共变性和爱因斯坦的等价性原理.
结论:
- 提出的框架成功地将非平衡热力学与内部变量集成到里曼几何中.
- 这种表述为分析曲时空中的热力学过程提供了一致的方法.
- 这些结果为相对论热力学和宇宙学的进一步研究提供了基础.
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