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Carlen, Jan Maas","submitted_at":"2012-03-24T01:45:59Z","abstract_excerpt":"Let $\\Cl$ denote the Clifford algebra over $\\R^n$, which is the von Neumann algebra generated by $n$ self-adjoint operators $Q_j$, $j=1,...,n$ satisfying the canonical anticommutation relations, $Q_iQ_j+Q_jQ_i = 2\\delta_{ij}I$, and let $\\tau$ denote the normalized trace on $\\Cl$. This algebra arises in quantum mechanics as the algebra of observables generated by $n$ Fermionic degrees of freedom. Let $\\Dens$ denote the set of all positive operators $\\rho\\in\\Cl$ such that $\\tau(\\rho) =1$; these are the non-commutative analogs of probability densities in the non-commutative probability space $(\\C"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1203.5377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-24T01:45:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"56c61ce6049ebe731d7ea27dbcf36e61a22c73ff89d5d36bb5f35063e092f709","abstract_canon_sha256":"582911ef76638912118a5f854c65838f1493ddf48a7ea47d7a20cd7158ce19af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:15.213739Z","signature_b64":"6+QGEN0KtBu0u6oO3cYur4FT6lzY1iRou4Xn1FzdAMksTZCuMiJpXgEeGO4YRZQkA/qg7wqQS5ZQXyIwdHqlCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bfda646f4a4d64c557ba6e282aa3ef040187f8cf0dab6639453df07cb8399dd","last_reissued_at":"2026-05-18T03:59:15.213212Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:15.213212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Analog of the 2-Wasserstein Metric in Non-commutative Probability under which the Fermionic Fokker-Planck Equation is Gradient Flow for the Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Eric A. 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