{"paper":{"title":"A Unified Gradient Theory for Frame-Indifferent Rates of Tensorial Internal Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Luis Espath","submitted_at":"2026-07-14T16:38:07Z","abstract_excerpt":"We develop a thermodynamically consistent framework for weakly nonlocal continua with tensor-valued internal variables. Let $\\boldsymbol{L}=\\operatorname{grad}\\boldsymbol{v}$, with stretching tensor $\\boldsymbol{D}=\\operatorname{sym}\\boldsymbol{L}$ and spin tensor $\\boldsymbol{W}=\\operatorname{skw}\\boldsymbol{L}$. We introduce the generators $\\boldsymbol{\\Gamma}_{\\alpha}=\\boldsymbol{W}+\\alpha\\boldsymbol{D}$, $\\alpha\\in\\{0,1\\}$, which unify corotational and upper-convected transport. The resulting kinematic structure induces canonical frame-indifferent evolutions of both the internal variable a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12949","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/2607.12949/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"}