{"paper":{"title":"The effects of the chemical potential in a BE distribution and the fractional parameter in a distribution with Mittag-Leffler function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","hep-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Minoru Biyajima, Naomichi Suzuki, Takuya Mizoguchi","submitted_at":"2015-04-06T10:29:40Z","abstract_excerpt":"The fractional Planck distribution is calculated by applying the Caputo fractional derivative with order $p$ ($p > 0$) to the equation proposed by Planck in 1900. In addition, the integral representation of the Mittag--Leffler function is employed to obtain a new formula for the fractional BE distribution, which is then used to analyze the NASA COBE monopole data. Based on this analysis, an identity $p\\simeq e^{-\\mu}$ is found, where $\\mu$ is the dimensionless constant chemical potential that was introduced to the BE distribution by the NASA COBE collaboration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01378","kind":"arxiv","version":2},"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"}