Uniqueness and characterization theorems for generalized entropies. (12th December 2017)

• Record Type: Journal Article
• Authors: Enciso, Alberto; Tempesta, Piergiulio
• Is Part Of: Journal of statistical mechanics. (2017:Dec.)
• Publication Date: 2017-12-12
• Subjects: 2; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa967f
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: The requirement that an entropy function be composable is key: it means that the entropy of a compound system can be calculated in terms of the entropy of its independent components. We prove that, under mild regularity assumptions, the only composable generalized entropy in trace form is the Tsallis one-parameter family (which contains Boltzmann–Gibbs as a particular case). This result leads to the use of generalized entropies that are not of trace form, such as Rényi's entropy, in the study of complex systems. In this direction, we also present a characterization theorem for a large class of composable non-trace-form entropy functions with features akin to those of Rényi's entropy.