{"id":"W4415710948","doi":"10.1007/s00220-025-05481-5","title":"Universal Chain Rules from Entropic Triangle Inequalities","year":2025,"lang":"en","type":"article","venue":"Communications in Mathematical Physics","topic":"Quantum Information and Cryptography","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"Natural Sciences and Engineering Research Council of Canada; Google","keywords":"Von Neumann entropy; Entropy (arrow of time); Von Neumann architecture; Upper and lower bounds; Entropic uncertainty; Quantum system; Quantum relative entropy; Generalized relative entropy","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000199668,0.00009722493,0.0001924021,0.0001329402,0.0001260261,0.0001144639,0.001913532,0.00004618687,0.00002315911],"category_scores_gemma":[0.00009646205,0.00009412249,0.00007851654,0.0006366552,0.0001501743,0.0004176834,0.000620952,0.0001808768,0.0001341371],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004577323,"about_ca_system_score_gemma":0.00005930817,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001875927,"about_ca_topic_score_gemma":0.000005717108,"domain_scores_codex":[0.9991078,0.0001484991,0.0003501889,0.0001152623,0.0001373032,0.0001409058],"domain_scores_gemma":[0.9974154,0.0006874928,0.00007803245,0.001730927,0.00005592883,0.00003217428],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000001190662,0.0001512603,0.00007662582,0.00001564597,0.00001220659,1.66484e-7,0.00217327,0.000009899797,0.00001413224,0.9894322,0.0002624326,0.007850927],"study_design_scores_gemma":[0.0003309043,0.000006560865,0.0003470343,0.00007811466,0.000005260931,1.173354e-7,0.0006219136,0.1149487,0.0001064982,0.8799478,0.00351897,0.00008811729],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01195863,0.0002064849,0.9387058,0.002561143,0.00006438304,0.0001629364,0.000008415873,0.0001466407,0.04618555],"genre_scores_gemma":[0.8447065,0.0001079625,0.154319,0.0006029226,0.00001627217,0.00004739522,0.00003628443,0.000005215393,0.0001583769],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8327479,"threshold_uncertainty_score":0.3838204,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03728938505453548,"score_gpt":0.2969629909032079,"score_spread":0.2596736058486724,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}