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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.
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From: Brian Zhang [view email]
[v1]Sun, 7 Apr 2019 22:39:00 UTC (51 KB)Full-text links:
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