a characterization of entropy in terms of information loss熵的特征信息丢失.pdfVIP

Entropy 2011, 13, 1945-1957; doi:10.3390/ OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article A Characterization of Entropy in Terms of Information Loss John C. Baez , Tobias Fritz and Tom Leinster Department of Mathematics, University of California, Riverside, CA 92521, USA; E-Mail: baez@ Centre for Quantum Technologies, National University of Singapore, 117543, Singapore ` ` Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, UK; E-Mail: tom.leinster@glasgow.ac.uk Author to whom correspondence should be addressed; E-Mail: tobias.fritz@icfo.es. Received: 11 October 2011; in revised form: 18 November 2011 / Accepted: 21 November 2011 / Published: 24 November 2011 Abstract: 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 the only concept of information loss that is functorial, convex