{"paper":{"title":"A Theorem on Ellipses, an Integrable System and a Theorem of Boltzmann","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Giovanni Gallavotti, Ian Jauslin","submitted_at":"2020-08-05T06:36:48Z","abstract_excerpt":"We study a mechanical system that was considered by Boltzmann in 1868 in the context of the derivation of the canonical and microcanonical ensembles. This system was introduced as an example of ergodic dynamics, which was central to Boltzmann's derivation. It consists of a single particle in two dimensions, which is subjected to a gravitational attraction to a fixed center. In addition, an infinite plane is fixed at some finite distance from the center, which acts as a hard wall on which the particle collides elastically. Finally, an extra centrifugal force is added. We will show that, in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.01955","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.01955/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}