{"paper":{"title":"Non-equilibrium steady state of the symmetric exclusion process with reservoirs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Adri\\'an Gonz\\'alez Casanova, Simone Floreani","submitted_at":"2023-07-05T17:55:39Z","abstract_excerpt":"Consider the open symmetric exclusion process on a connected graph with vertexes in $[N-1]:=\\{1,\\ldots, N-1\\}$ where points $1$ and $N-1$ are connected, respectively, to a left reservoir and a right reservoir with densities $\\rho_L,\\rho_R\\in(0,1)$. We prove that the non-equilibrium steady state of such system is $$\\mu_{\\text{stat}} = \\sum_{I\\subset \\mathcal P([N-1]) }F(I)\\bigg(\\otimes_{x\\in I}\\rm{Bernoulli}(\\rho_R)\\otimes_{y\\in [N-1]\\setminus I}\\rm{Bernoulli}(\\rho_L) \\bigg).$$ In the formula above $ \\mathcal P([N-1])$ denotes the power set of $[N-1]$ while the numbers $F(I)> 0$ are such that $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.02481","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/2307.02481/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"}