{"paper":{"title":"Coconuts and Islanders: A Statistics-First Guide to the Boltzmann Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.ed-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Brian Zhang","submitted_at":"2019-04-07T22:39:00Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04669","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}