{"id":"W4416827696","doi":"10.5539/ijsp.v14n4p1","title":"The Extended H Theorem and the Extended Entropy","year":2025,"lang":"","type":"article","venue":"International Journal of Statistics and Probability","topic":"Statistical Mechanics and Entropy","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Entropy (arrow of time); H-theorem; Maxwell–Boltzmann distribution; Maximum entropy probability distribution; Entropy rate; Joint quantum entropy; Distribution function; Min entropy; Maximum entropy thermodynamics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002059203,0.0002592134,0.0004280999,0.00005717062,0.0004939559,0.0007446025,0.0005835536,0.00006011128,0.0001424454],"category_scores_gemma":[0.0009511422,0.0001394206,0.0001465865,0.00009358954,0.001166834,0.00009819599,0.0002989623,0.0005647195,0.000002455186],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007758226,"about_ca_system_score_gemma":0.0002830024,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006188859,"about_ca_topic_score_gemma":0.000006351449,"domain_scores_codex":[0.9973796,0.0004128714,0.001086678,0.0002684946,0.0005566206,0.0002957575],"domain_scores_gemma":[0.9939593,0.003770346,0.000669433,0.0002450391,0.001213663,0.0001422054],"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":[0.001381612,0.0001380924,0.0005018809,0.0000219479,0.0006587658,0.000007774432,0.0001968075,0.000006762124,0.00001270619,0.7628978,0.001050509,0.2331253],"study_design_scores_gemma":[0.003199117,0.0001536801,0.007482818,0.0001077781,0.0002496463,0.00001765108,0.0003500814,0.02384833,0.00003373257,0.9499843,0.01444636,0.0001265224],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01533387,0.004276963,0.9520835,0.02000567,0.004575199,0.00069453,0.001235571,0.000005297905,0.001789435],"genre_scores_gemma":[0.9892303,0.002772706,0.006888561,0.0002655289,0.000448002,0.00001275383,0.000009495567,0.00001198695,0.0003607115],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9738964,"threshold_uncertainty_score":0.7180219,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007313362140513064,"score_gpt":0.273247997312922,"score_spread":0.2659346351724089,"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."}}