{"paper":{"title":"Class of consistent fundamental-measure free energies for hard-sphere mixtures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.chem-ph"],"primary_cat":"cond-mat.soft","authors_text":"Andr\\'es Santos","submitted_at":"2012-08-15T10:57:28Z","abstract_excerpt":"In fundamental-measure theories the bulk excess free-energy density of a hard-sphere fluid mixture is assumed to depend on the partial number densities ${\\rho_i}$ only through the four scaled-particle-theory variables ${\\xi_\\alpha}$, i.e., $\\Phi({\\rho_i})\\to\\Phi({\\xi_\\alpha})$. By imposing consistency conditions, it is proven here that such a dependence must necessarily have the form $\\Phi({\\xi_\\alpha})=-\\xi_0\\ln(1-\\xi_3)+\\Psi(y)\\xi_1\\xi_2/(1-\\xi_3)$, where $y\\equiv {\\xi_2^2}/{12\\pi \\xi_1 (1-\\xi_3)}$ is a scaled variable and $\\Psi(y)$ is an arbitrary dimensionless scaling function which can be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3089","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"}