文章基本信息

标题：Generalized entropies and logarithms and their duality relations
本地全文：下载
作者：Rudolf Hanel ; Stefan Thurner ; Murray Gell-Mann 等
期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2012
卷号：109
期号：47
页码：19151-19154
DOI：10.1073/pnas.1216885109
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with these generalized entropies, making them useful for understanding distribution functions of non-Markovian or nonergodic complex systems. For such systems where the composability axiom is violated there exist only two ways to implement the maximum entropy principle, one using escort probabilities, the other not. The two ways are connected through a duality. Here we show that this duality fixes a unique escort probability, which allows us to derive a complete theory of the generalized logarithms that naturally arise from the violation of this axiom. We then show how the functional forms of these generalized logarithms are related to the asymptotic scaling behavior of the entropy.
关键词：classical statistical mechanics ; correlated systems