{"id":"W2094613524","doi":"10.1103/physreve.69.021109","title":"Generalized bracket formulation of constrained dynamics in phase space","year":2004,"lang":"en","type":"article","venue":"Physical Review E","topic":"Advanced Thermodynamics and Statistical Mechanics","field":"Physics and Astronomy","cited_by":22,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Phase space; Poisson bracket; Holonomic constraints; Mathematics; Bracket; Formalism (music); Hamiltonian mechanics; Invariant (physics); Holonomic; Hamiltonian (control theory); Dynamical systems theory; Classical mechanics; Hamiltonian system; Statistical mechanics; Statistical physics; Mathematical analysis; Physics; Mathematical physics; Pure mathematics; Mathematical optimization; Quantum mechanics; Lie algebra","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008760008,0.0007802128,0.0007267842,0.001048922,0.0009548627,0.001576358,0.0008854699,0.000922999,0.006217381],"category_scores_gemma":[0.0009715512,0.0002675037,0.0007190508,0.0008853522,0.002281644,0.003899151,0.00131986,0.001243605,0.0009959205],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007886441,"about_ca_system_score_gemma":0.0008888867,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001241977,"about_ca_topic_score_gemma":0.000890861,"domain_scores_codex":[0.999488,0.0001545206,0.00002988526,0.0001008458,0.0001689275,0.00005777694],"domain_scores_gemma":[0.999638,0.00007719859,0.00006154022,0.00005508828,0.0001012781,0.00006695294],"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":[0.000002145884,0.000002149366,0.00001672349,0.000009517185,0.000002451751,0.00002456677,0.00004851901,0.001455591,0.0004975097,0.9966553,0.0002972692,0.0009881803],"study_design_scores_gemma":[0.000003815388,0.00001557889,0.00004941603,0.000006921951,0.000002380038,0.00005384946,0.00002575096,0.02065304,0.0001915949,0.97469,0.004299264,0.0000084146],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05762899,0.003053403,0.8696636,0.001977633,0.0009177715,0.0001008427,0.0004087894,0.0002038511,0.06604521],"genre_scores_gemma":[0.7738186,0.003693025,0.1718291,0.0012637,0.001641303,0.0003855124,0.0004378487,0.0003079376,0.04662297],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006217381,"threshold_uncertainty_score":0.02079922,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01390014014517405,"score_gpt":0.335919259964947,"score_spread":0.3220191198197729,"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."}}