{"paper":{"title":"A second order equation for Schr\\\"odinger bridges with applications to the hot gas experiment and entropic transportation cost","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Giovanni Conforti","submitted_at":"2017-04-16T21:20:32Z","abstract_excerpt":"The \\emph{Schr\\\"odinger problem} is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schr\\\"odinger as the problem of describing the most likely evolution of a large number of Brownian particles conditioned to reach an \"unexpected configuration\". Its optimal value, the \\textit{entropic transportation cost}, and its optimal solution, the \\textit{Schr\\\"odinger bridge}, stand as the natural probabilistic counterparts to the transportation cost and displacement interpolation. Moreover, they provide a natural way of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04821","kind":"arxiv","version":4},"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"}