{"paper":{"title":"Entropy production and the geometry of dissipative evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Celia Reina, Johannes Zimmer","submitted_at":"2015-07-01T22:09:11Z","abstract_excerpt":"Purely dissipative evolution equations are often cast as gradient flow structures, $\\dot{\\mathbf{z}}=K(\\mathbf{z})DS(\\mathbf{z})$, where the variable $\\mathbf{z}$ of interest evolves towards the maximum of a functional $S$ according to a metric defined by an operator $K$. While the functional often follows immediately from physical considerations (e.g., the thermodynamic entropy), the operator $K$ and the associated geometry does not necessarily so (e.g., Wasserstein geometry for diffusion). In this paper, we present a variational statement in the sense of maximum entropy production that direc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01014","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":""},"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"}