{"paper":{"title":"Gradient flow structure and exponential decay of the sandwiched R\\'enyi divergence for primitive Lindblad equations with GNS-detailed balance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Jianfeng Lu, Yu Cao, Yulong Lu","submitted_at":"2018-10-01T18:21:02Z","abstract_excerpt":"We study the entropy production of the sandwiched R\\'enyi divergence under the primitive Lindblad equation with GNS-detailed balance. We prove that the Lindblad equation can be identified as the gradient flow of the sandwiched R\\'enyi divergence of any order ${\\alpha} \\in (0, \\infty)$. This extends a previous result by Carlen and Maas [Journal of Functional Analysis, 273(5), 1810-1869] for the quantum relative entropy (i.e., ${\\alpha} = 1$). Moreover, we show that the sandwiched R\\'enyi divergence of any order ${\\alpha} \\in (0, \\infty)$ decays exponentially fast under the time-evolution of suc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00906","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"}