2born (2born) wrote,

Самый странный способ вывести распределение Больцмана

Coconuts and Islanders: A Statistics-First Guide to the Boltzmann Distribution: https://arxiv.org/abs/1904.04669

The Boltzmann distribution is one of the key equations of thermal physics and is widely used in machine learning as well. Here I derive a Boltzmann distribution in a simple pedagogical example using only tools from a first-year probability course. The example is called "coconuts and islanders" and was taught to me by my father, Shoucheng Zhang (1963 - 2018), to whom these notes are dedicated. By focusing on this simple story, which can be easily simulated on a computer, I aim to provide a more accessible and intuitive presentation of the Boltzmann distribution. Yet I hope this exposition also inspires deep thinking about statistical physics. For instance, I show that the coconuts and islanders story illuminates a connection between the "fundamental assumption of statistical mechanics"---all microstates are equally probable---and the statistical property of detailed balance.

Немаленькая заметка, 28 страниц, Оксфорд - не хухры-мухры:)) Но, как минимум, коллекцией примеров и ссылок будет, несомненно, полезна.
Tags: Мегаучебник или Что я читал и похвалил, образование, популяризация, постигая статистику, разгребая arXiv'ы

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