Coconuts and Islanders: A StatisticsFirst Guide to the Boltzmann Distribution
Abstract
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 firstyear 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 probableand the statistical property of detailed balance.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.04669
 Bibcode:
 2019arXiv190404669Z
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Physics  Physics Education