BOUNDS ON DIVERGENCE IN NONEXTENSIVE STATISTICAL MECHANICS

Takuya Yamano

doi:10.22342/jims.19.2.165.89-97

Takuya Yamano ⁽¹⁾

(1) Department of Information Sciences, Faculty of Science, Kanagawa University, Japan

https://doi.org/10.22342/jims.19.2.165.89-97

Issue
Volume 19 Number 2 (October 2013)

Submitted
March 4, 2014

Accepted
March 4, 2014

Published
March 4, 2014

Keywords:

Information divergences, Relative entropies, Generalized divergences

PDF

Abstract

We focus on an important property upon generalization of the Kullback-Leibler divergence used in nonextensive statistical mechanics, i.e., bounds. Weexplicitly show upper and lower bounds on it in terms of existing familiar divergences based on the ﬁnite range of the probability distribution ratio. This provides a link between the observed distribution functions based on histograms of events and parameterized distance measures in physical sciences. The charactering parameter q < 0 and q > 1 are rejected from the consideration of bounded divergence.

DOI : http://dx.doi.org/10.22342/jims.19.2.165.89-97

Full text article

Generated from XML file

Authors

Takuya Yamano

Department of Information Sciences, Faculty of Science, Kanagawa University

yamano@amy.hi-ho.ne.jp (Primary Contact)

Yamano, T. (2014). BOUNDS ON DIVERGENCE IN NONEXTENSIVE STATISTICAL MECHANICS. Journal of the Indonesian Mathematical Society, 19(2), 89–97. https://doi.org/10.22342/jims.19.2.165.89-97