BOUNDS ON DIVERGENCE IN NONEXTENSIVE STATISTICAL MECHANICS

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