{"paper":{"title":"Grand-Canonical Typicality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Cedric Igelspacher, Cornelia Vogel, Roderich Tumulka","submitted_at":"2026-01-06T18:57:29Z","abstract_excerpt":"We study how the grand-canonical density matrix arises in macroscopic quantum systems. ``Canonical typicality'' is the known statement that for a typical wave function $\\Psi$ from a micro-canonical energy shell of a quantum system $S$ weakly coupled to a large but finite quantum system $B$, the reduced density matrix $\\hat{\\rho}^S_\\Psi=\\mathrm{tr}^B |\\Psi\\rangle\\langle \\Psi|$ is approximately equal to the canonical density matrix $\\hat{\\rho}_\\mathrm{can}=Z^{-1}_\\mathrm{can} \\exp(-\\beta \\hat{H}^S)$. Here, we discuss the analogous statement and related questions for the \\emph{grand-canonical} de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.03253","kind":"arxiv","version":3},"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/2601.03253/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"}