连接统计力学与黑洞演化：理论形式体系
Bridging Between Statistical Mechanics and Black Hole Evolution: Theoretical Formalism
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中文总结 AI 辅助
本文首次用统计力学（Kramers-Moyal展开）描述黑洞分布函数随质量与时间的演化，连接微观随机过程与宏观演化，为数据驱动理解黑洞物理提供新框架。
中文摘要 AI 辅助
宇宙中的黑洞在质量上跨越近十个数量级，并在一个巨大的宇宙时间尺度上存在，其历史至少可追溯至宇宙早期，当时宇宙仅有几亿年历史。这些天体的形成与演化至今仍是一个谜，因为没有任何直接探测手段能够追踪整个质量范围和宇宙时间内的每一个黑洞。本研究首次展示了黑洞演化的统计力学描述。我表明，尽管每个黑洞及其演化受随机过程支配，但可以对宇宙中黑洞的分布函数进行宏观描述，且其在整个质量范围和宇宙时间内的演化可以用Kramers-Moyal展开来表达。这种通过Kramers-Moyal展开将统计力学与黑洞演化相连接的桥梁，使得发现黑洞演化中起作用的潜在物理过程成为可能。未来，将该技术应用于来自不同信使（如引力波和电磁波）的可获取数据（这些信使探测宇宙中的黑洞），可以在不了解潜在微观随机过程的情况下，通过这种统计力学技术实现对潜在物理过程的数据驱动理解。
英文摘要
Black holes in the Universe span nearly ten orders of magnitude in mass over a large cosmic timescale, dating back to at least the Universe's early history, when it was only a few hundred million years old. The formation and evolution of these objects remain a mystery because no direct probe can trace each black hole across the full mass range and cosmic time. This work shows, for the first time, a statistical mechanical description of black hole evolution. I show that though each black hole and its evolution are governed by stochastic processes, one can make a macroscopic description of the distribution function of black holes in the Universe, and its evolution over the entire mass range and cosmic time can be expressed in terms of the Kramers-Moyal expansion. This bridging between statistical mechanics and black hole evolution in terms of the Kramers-Moyal expansion enables the discovery of the underlying physical processes that play a role in the evolution of black holes. In the future, the application of this technique to data accessible from different messengers, such as gravitational waves and electromagnetic waves, which probe black holes in the Universe, can lead to a data-driven understanding of the underlying physical processes by this statistical mechanics technique despite the ignorance of the underlying microscopic stochastic processes.
发表机构
- Tata Institute of Fundamental Research（塔塔基础研究所）
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