A theorem on the existence of trace-form generalized entropies

作者：Tempesta Piergiulio^*

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2015, 471(2183): 20150165.

DOI：10.1098/rspa.2015.0165

• generalized entropies
• group theory
• composability
• geometric information theory

An analytic technique is proposed, which allows to generate many new examples of entropic functionals generalizing the standard Boltzmann-Gibbs entropy. Our approach is based on the existence of a grouptheoretical structure, which is intimately related with the notion of entropy, as clarified in recent work of the author. The new entropies proposed satisfy the first three Shannon-Khinchin axioms and are composable (at least in a weak sense). By combining them, multiparametric examples of entropies can be realized. As a by-product of the theory, entropic functionals related to the Riemann zeta function and other numbertheoretical functions are introduced.

• 出版日期2015-11-8