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Abstract: The Boltzmann distribution is one of the key equations of thermal physics andis widely used in machine learning as well. Here I derive a Boltzmanndistribution in a simple pedagogical example using only tools from a first-yearprobability course. The example is called 'coconuts and islanders' and wastaught to me by my father, Shoucheng Zhang (1963 - 2018), to whom these notesare dedicated. By focusing on this simple story, which can be easily simulatedon a computer, I aim to provide a more accessible and intuitive presentation ofthe Boltzmann distribution. Yet I hope this exposition also inspires deepthinking about statistical physics. For instance, I show that the coconuts andislanders story illuminates a connection between the 'fundamental assumption ofstatistical mechanics'---all microstates are equally probable---and thestatistical property of detailed balance.
Submission history
From: Brian Zhang [view email][v1]Sun, 7 Apr 2019 22:39:00 UTC (51 KB)
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Bibliographic ToolsAbstract: The Boltzmann distribution is one of the key equations of thermal physics andis widely used in machine learning as well. Here I derive a Boltzmanndistribution in a simple pedagogical example using only tools from a first-yearprobability course. The example is called 'coconuts and islanders' and wastaught to me by my father, Shoucheng Zhang (1963 - 2018), to whom these notesare dedicated. By focusing on this simple story, which can be easily simulatedon a computer, I aim to provide a more accessible and intuitive presentation ofthe Boltzmann distribution. Yet I hope this exposition also inspires deepthinking about statistical physics. For instance, I show that the coconuts andislanders story illuminates a connection between the 'fundamental assumption ofstatistical mechanics'---all microstates are equally probable---and thestatistical property of detailed balance.
Submission history
From: Brian Zhang [view email][v1]Sun, 7 Apr 2019 22:39:00 UTC (51 KB)
Full-text links:
Download:
Current browse context:References & Citations
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs and how to get involved.
Bibliographic ToolsPlatform: PC
Release Date: 04.04.2019