BOUNDS ON DIVERGENCE IN NONEXTENSIVE STATISTICAL MECHANICS

Takuya Yamano (Department of Information Sciences, Faculty of Science, Kanagawa University)

Journal of the Indonesian Mathematical Society
Volume 19 Number 2 (October 2013)

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