{"paper":{"title":"A Characterization of Entropy in Terms of Information Loss","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.IT","math.MP","quant-ph"],"primary_cat":"cs.IT","authors_text":"John C. Baez, Tobias Fritz, Tom Leinster","submitted_at":"2011-06-09T12:47:00Z","abstract_excerpt":"There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the entropy of a probability measure on a finite set, this characterization focuses on the `information loss', or change in entropy, associated with a measure-preserving function. Information loss is a special case of conditional entropy: namely, it is the entropy of a random variable conditioned on some function of that variable. We show that Shannon entropy gives "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1791","kind":"arxiv","version":3},"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"}